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Статті в журналах з теми "Matching"

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Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 8 червня 2024

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1

CHENG, EDDIE, and SACHIN PADMANABHAN. "MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR CROSSED CUBES." Parallel Processing Letters 22, no. 02 (May 16, 2012): 1250005. http://dx.doi.org/10.1142/s0129626412500053.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this paper, we find the matching preclusion number and the conditional matching preclusion number with the classification of the optimal sets for the class of crossed cubes, an important variant of the class of hypercubes. Indeed, we will establish more general results on the matching preclusion and the conditional matching preclusion problems for a larger class of interconnection networks.

2

Chen, Ciping. "Matchings and matching extensions in graphs." Discrete Mathematics 186, no. 1-3 (May 1998): 95–103. http://dx.doi.org/10.1016/s0012-365x(97)00182-9.

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3

MAO, YAPING, and EDDIE CHENG. "A Concise Survey of Matching Preclusion in Interconnection Networks." Journal of Interconnection Networks 19, no. 03 (September 2019): 1940006. http://dx.doi.org/10.1142/s0219265919400061.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. There are other related parameters and generalization including the strong matching preclusion number, the conditional matching preclusion number, the fractional matching preclusion number, and so on. In this survey, we give an introduction on the general topic of matching preclusion.

4

LÜ, HUAZHONG, and TINGZENG WU. "Fractional Matching Preclusion for Restricted Hypercube-Like Graphs." Journal of Interconnection Networks 19, no. 03 (September 2019): 1940010. http://dx.doi.org/10.1142/s0219265919400103.

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The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, which extend some known results.

5

Echenique, Federico, SangMok Lee, Matthew Shum, and M. Bumin Yenmez. "Stability and Median Rationalizability for Aggregate Matchings." Games 12, no. 2 (April 9, 2021): 33. http://dx.doi.org/10.3390/g12020033.

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We develop the theory of stability for aggregate matchings used in empirical studies and establish fundamental properties of stable matchings including the result that the set of stable matchings is a non-empty, complete, and distributive lattice. Aggregate matchings are relevant as matching data in revealed preference theory. We present a result on rationalizing a matching data as the median stable matching.

6

Cannas, Massimo, and Emiliano Sironi. "Optimal Matching with Matching Priority." Analytics 3, no. 1 (March 19, 2024): 165–77. http://dx.doi.org/10.3390/analytics3010009.

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Matching algorithms are commonly used to build comparable subsets (matchings) in observational studies. When a complete matching is not possible, some units must necessarily be excluded from the final matching. This may bias the final estimates comparing the two populations, and thus it is important to reduce the number of drops to avoid unsatisfactory results. Greedy matching algorithms may not reach the maximum matching size, thus dropping more units than necessary. Optimal matching algorithms do ensure a maximum matching size, but they implicitly assume that all units have the same matching priority. In this paper, we propose a matching strategy which is order optimal in the sense that it finds a maximum matching size which is consistent with a given matching priority. The strategy is based on an order-optimal matching algorithm originally proposed in connection with assignment problems by D. Gale. When a matching priority is given, the algorithm ensures that the discarded units have the lowest possible matching priority. We discuss the algorithm’s complexity and its relation with classic optimal matching. We illustrate its use with a problem in a case study concerning a comparison of female and male executives and a simulation.

7

CHENG, EDDIE, RANDY JIA, and DAVID LU. "MATCHING PRECLUSION AND CONDITIONAL MATCHING PRECLUSION FOR AUGMENTED CUBES." Journal of Interconnection Networks 11, no. 01n02 (March 2010): 35–60. http://dx.doi.org/10.1142/s0219265910002726.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those incident to a single vertex. Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those incident to a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number and classify all optimal sets for the augmented cubes, a class of networks designed as an improvement of the hypercubes.

8

Wang, Xia, Tianlong Ma, Jun Yin, and Chengfu Ye. "Fractional matching preclusion for radix triangular mesh." Discrete Mathematics, Algorithms and Applications 11, no. 04 (August 2019): 1950048. http://dx.doi.org/10.1142/s1793830919500484.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the radix triangular mesh [Formula: see text], and all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.

9

Anantapantula, Sai, Christopher Melekian, and Eddie Cheng. "Matching Preclusion for the Shuffle-Cubes." Parallel Processing Letters 28, no. 03 (September 2018): 1850012. http://dx.doi.org/10.1142/s0129626418500123.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. A graph is maximally matched if its matching preclusion number is equal to its minimum degree, and is super matched if the matching preclusion number can only be achieved by deleting all edges incident to a single vertex. In this paper, we determine the matching preclusion number and classify the optimal matching preclusion sets for the shuffle-cube graphs, a variant of the well-known hypercubes.

10

Greinecker, Michael, and Christopher Kah. "Pairwise Stable Matching in Large Economies." Econometrica 89, no. 6 (2021): 2929–74. http://dx.doi.org/10.3982/ecta16228.

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We formulate a stability notion for two‐sided pairwise matching problems with individually insignificant agents in distributional form. Matchings are formulated as joint distributions over the characteristics of the populations to be matched. Spaces of characteristics can be high‐dimensional and need not be compact. Stable matchings exist with and without transfers, and stable matchings correspond precisely to limits of stable matchings for finite‐agent models. We can embed existing continuum matching models and stability notions with transferable utility as special cases of our model and stability notion. In contrast to finite‐agent matching models, stable matchings exist under a general class of externalities.

11

Ma, Tianlong, Yaping Mao, Eddie Cheng, and Jinling Wang. "Fractional Matching Preclusion for (n, k)-Star Graphs." Parallel Processing Letters 28, no. 04 (December 2018): 1850017. http://dx.doi.org/10.1142/s0129626418500172.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu introduced the concept of fractional matching preclusion number in 2017. The Fractional Matching Preclusion Number (FMP number) of G is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The Fractional Strong Matching Preclusion Number (FSMP number) of G is the minimum number of vertices and/or edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the FMP number and the FSMP number for (n, k)-star graphs. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.

12

He, Jinghua, Erling Wei, Dong Ye, and Shaohui Zhai. "On perfect matchings in matching covered graphs." Journal of Graph Theory 90, no. 4 (October 2, 2018): 535–46. http://dx.doi.org/10.1002/jgt.22411.

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13

Kolupaev, Dmitriy, and Andrey Kupavskii. "Erdős matching conjecture for almost perfect matchings." Discrete Mathematics 346, no. 4 (April 2023): 113304. http://dx.doi.org/10.1016/j.disc.2022.113304.

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14

Zhang, Shuangshuang, Yuzhi Xiao, Xia Liu, and Jun Yin. "A Short Note of Strong Matching Preclusion for a Class of Arrangement Graphs." Parallel Processing Letters 30, no. 01 (March 2020): 2050001. http://dx.doi.org/10.1142/s0129626420500012.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. The strong matching preclusion is a well-studied measure for the network invulnerability in the event of edge failure. In this paper, we obtain the strong matching preclusion number for a class of arrangement graphs and categorize their the strong matching preclusion set, which are a supplement of known results.

15

Khalashi Ghezelahmad, Somayeh. "On matching integral graphs." Mathematical Sciences 13, no. 4 (October 14, 2019): 387–94. http://dx.doi.org/10.1007/s40096-019-00307-7.

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Abstract The matching polynomial of a graph has coefficients that give the number of matchings in the graph. In this paper, we determine all connected graphs on eight vertices whose matching polynomials have only integer zeros. A graph is matching integral if the zeros of its matching polynomial are all integers. We show that there are exactly two matching integral graphs on eight vertices.

16

CHENG, EDDIE, DAVID LU, and BRIAN XU. "STRONG MATCHING PRECLUSION OF PANCAKE GRAPHS." Journal of Interconnection Networks 14, no. 02 (June 2013): 1350007. http://dx.doi.org/10.1142/s0219265913500072.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. In this paper, we examine the properties of pancake graphs by finding its strong matching preclusion number and categorizing all optimal solutions.

17

BONNEVILLE, PHILIP, EDDIE CHENG, and JOSEPH RENZI. "STRONG MATCHING PRECLUSION FOR THE ALTERNATING GROUP GRAPHS AND SPLIT-STARS." Journal of Interconnection Networks 12, no. 04 (December 2011): 277–98. http://dx.doi.org/10.1142/s0219265911003003.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem and has recently been introduced by Park and Ihm.15 In this paper, we examine properties of strong matching preclusion for alternating group graphs, by finding their strong matching preclusion numbers and categorizing all optimal solutions. More importantly, we prove a general result on taking a Cartesian product of a graph with K2 (an edge) to obtain the corresponding results for split-stars.

18

CHENG, EDDIE, and OMER SIDDIQUI. "Strong Matching Preclusion of Arrangement Graphs." Journal of Interconnection Networks 16, no. 02 (June 2016): 1650004. http://dx.doi.org/10.1142/s0219265916500043.

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The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph with neither perfect matchings nor almost-perfect matchings. This is an extension of the matching preclusion problem that was introduced by Park and Ihm. The class of arrangement graphs was introduced as a common generalization of the star graphs and alternating group graphs, and to provide an even richer class of interconnection networks. In this paper, the goal is to find the strong matching preclusion number of arrangement graphs and to categorize all optimal strong matching preclusion sets of these graphs.

19

Faenza, Yuri, and Telikepalli Kavitha. "Quasi-Popular Matchings, Optimality, and Extended Formulations." Mathematics of Operations Research 47, no. 1 (February 2022): 427–57. http://dx.doi.org/10.1287/moor.2021.1139.

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Let [Formula: see text] be an instance of the stable marriage problem in which every vertex ranks its neighbors in a strict order of preference. A matching [Formula: see text] in [Formula: see text] is popular if [Formula: see text] does not lose a head-to-head election against any matching. Popular matchings generalize stable matchings. Unfortunately, when there are edge costs, to find or even approximate up to any factor a popular matching of minimum cost is NP-hard. Let [Formula: see text] be the cost of a min-cost popular matching. Our goal is to efficiently compute a matching of cost at most [Formula: see text] by paying the price of mildly relaxing popularity. Our main positive results are two bicriteria algorithms that find in polynomial time a “quasi-popular” matching of cost at most [Formula: see text]. Moreover, one of the algorithms finds a quasi-popular matching of cost at most that of a min-cost popular fractional matching, which could be much smaller than [Formula: see text]. Key to the other algorithm is a polynomial-size extended formulation for an integral polytope sandwiched between the popular and quasi-popular matching polytopes. We complement these results by showing that it is NP-hard to find a quasi-popular matching of minimum cost and that both the popular and quasi-popular matching polytopes have near-exponential extension complexity.

20

de Fez, M. D., P. Capilla, M. J. Luque, J. Pérez-Carpinell, and J. C. del Pozo. "Asymmetric colour matching: Memory matching versus simultaneous matching." Color Research & Application 26, no. 6 (October 8, 2001): 458–68. http://dx.doi.org/10.1002/col.1066.

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21

Noureen, Sadia, and Bhatti Ahmad. "The modified first Zagreb connection index and the trees with given order and size of matchings." Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics 13, no. 2 (2021): 85–94. http://dx.doi.org/10.5937/spsunp2102085n.

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A subset of the edge set of a graph G is called a matching in G if its elements are not adjacent in G. A matching in G with the maximum cardinality among all the matchings in G is called a maximum matching. The matching number in the graph G is the number of elements in the maximum matching of G. This present paper is devoted to the investigation of the trees, which maximize the modified first Zagreb connection index among the trees with a given order and matching number.

22

WANG, YANCHUN, WEIGANG SUN, JINGYUAN ZHANG, and SEN QIN. "ON THE CONDITIONAL MATCHING OF FRACTAL NETWORKS." Fractals 24, no. 04 (December 2016): 1650054. http://dx.doi.org/10.1142/s0218348x16500547.

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In this paper, we propose a new matching (called a conditional matching), where the condition refers to the matching of the new constructed network which includes all the nodes in the original network. We then enumerate the conditional matchings of the new network and prove that the number of conditional matchings is just the product of degree sequences of the original network. We choose two families of fractal networks to show our obtained results, including the pseudofractal network and Cayley tree. Finally, we calculate the entropy of the conditional matchings on the considered networks and see that the entropy of Cayley tree is smaller than that of the pseudofractal network.

23

Doval, Laura. "Dynamically stable matching." Theoretical Economics 17, no. 2 (2022): 687–724. http://dx.doi.org/10.3982/te4187.

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I introduce a stability notion, dynamic stability, for two‐sided dynamic matching markets where (i) matching opportunities arrive over time, (ii) matching is one‐to‐one, and (iii) matching is irreversible. The definition addresses two conceptual issues. First, since not all agents are available to match at the same time, one must establish which agents are allowed to form blocking pairs. Second, dynamic matching markets exhibit a form of externality that is not present in static markets: an agent's payoff from remaining unmatched cannot be defined independently of other contemporaneous agents' outcomes. Dynamically stable matchings always exist. Dynamic stability is a necessary condition to ensure timely participation in the economy by ensuring that agents do not strategically delay the time at which they are available to match.

24

Reny, Philip J. "Efficient Matching in the School Choice Problem." American Economic Review 112, no. 6 (June 1, 2022): 2025–43. http://dx.doi.org/10.1257/aer.20210240.

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Stable matchings in school choice needn’t be Pareto efficient and can leave thousands of students worse off than necessary. Call a matching μ priority-neutral if no matching can make any student whose priority is violated by μ better off without violating the priority of some student who is made worse off. Call a matching priority-efficient if it is priority-neutral and Pareto efficient. We show that there is a unique priority-efficient matching and that it dominates every priority-neutral matching and every stable matching. Moreover, truth-telling is a maxmin optimal strategy for every student in the mechanism that selects the priority-efficient matching. (JEL C78, I21, I28)

25

Pálvölgyi, Dömötör. "Partitioning to three matchings of given size is NP-complete for bipartite graphs." Acta Universitatis Sapientiae, Informatica 6, no. 2 (December 1, 2014): 206–9. http://dx.doi.org/10.1515/ausi-2015-0004.

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Abstract We show that the problem of deciding whether the edge set of a bipartite graph can be partitioned into three matchings, of size k1, k2 and k3 is NP-complete, even if one of the matchings is required to be perfect. We also show that the problem of deciding whether the edge set of a simple graph contains a perfect matching and a disjoint matching of size k or not is NP-complete, already for bipartite graphs with maximum degree 3. It also follows from our construction that it is NP-complete to decide whether in a bipartite graph there is a perfect matching and a disjoint matching that covers all vertices whose degree is at least 2.

26

Demuynck, Thomas, and Umutcan Salman. "On the revealed preference analysis of stable aggregate matchings." Theoretical Economics 17, no. 4 (2022): 1651–82. http://dx.doi.org/10.3982/te4723.

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Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable and nontransferable utility and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalizable. For matchings that are not rationalizable, we provide a simple greedy algorithm that computes the minimum number of matches that need to be removed to obtain a rationalizable matching. We also show that the related problem of finding the minimum number of types that we need to remove in order to obtain a rationalizable matching is NP‐complete.

27

Lo, Allan. "Existences of rainbow matchings and rainbow matching covers." Discrete Mathematics 338, no. 11 (November 2015): 2119–24. http://dx.doi.org/10.1016/j.disc.2015.05.015.

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28

Hosseini, Hadi, Zhiyi Huang, Ayumi Igarashi, and Nisarg Shah. "Class Fairness in Online Matching." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 5 (June 26, 2023): 5673–80. http://dx.doi.org/10.1609/aaai.v37i5.25704.

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We initiate the study of fairness among classes of agents in online bipartite matching where there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online and must be matched irrevocably upon arrival. In this setting, agents are partitioned into a set of classes and the matching is required to be fair with respect to the classes. We adopt popular fairness notions (e.g. envy-freeness, proportionality, and maximin share) and their relaxations to this setting and study deterministic and randomized algorithms for matching indivisible items (leading to integral matchings) and for matching divisible items (leading to fractional matchings). For matching indivisible items, we propose an adaptive-priority-based algorithm, MATCH-AND-SHIFT, prove that it achieves (1/2)-approximation of both class envy-freeness up to one item and class maximin share fairness, and show that each guarantee is tight. For matching divisible items, we design a water-filling-based algorithm, EQUAL-FILLING, that achieves (1-1/e)-approximation of class envy-freeness and class proportionality; we prove (1-1/e) to be tight for class proportionality and establish a 3/4 upper bound on class envy-freeness.

29

Alishahi, Meysam, and Hajiabolhassan Hossein. "On the Chromatic Number of Matching Kneser Graphs." Combinatorics, Probability and Computing 29, no. 1 (September 12, 2019): 1–21. http://dx.doi.org/10.1017/s0963548319000178.

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AbstractIn an earlier paper, the present authors (2015) introduced the altermatic number of graphs and used Tucker’s lemma, an equivalent combinatorial version of the Borsuk–Ulam theorem, to prove that the altermatic number is a lower bound for chromatic number. A matching Kneser graph is a graph whose vertex set consists of all matchings of a specified size in a host graph and two vertices are adjacent if their corresponding matchings are edge-disjoint. Some well-known families of graphs such as Kneser graphs, Schrijver graphs and permutation graphs can be represented by matching Kneser graphs. In this paper, unifying and generalizing some earlier works by Lovász (1978) and Schrijver (1978), we determine the chromatic number of a large family of matching Kneser graphs by specifying their altermatic number. In particular, we determine the chromatic number of these matching Kneser graphs in terms of the generalized Turán number of matchings.

30

CHENG, EDDIE, and LÁSZLÓ LIPTÁK. "CONDITIONAL MATCHING PRECLUSION FOR (n,k)-STAR GRAPHS." Parallel Processing Letters 23, no. 01 (March 2013): 1350004. http://dx.doi.org/10.1142/s0129626413500047.

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The matching preclusion number of an even graph G, denoted by mp (G), is the minimum number of edges whose deletion leaves the resulting graph without perfect matchings. The conditional matching preclusion number of an even graph G, denoted by mp 1(G), is the minimum number of edges whose deletion leaves the resulting graph with neither perfect matchings nor isolated vertices. The class of (n,k)-star graphs is a popular class of interconnection networks for which the matching preclusion number and the classification of the corresponding optimal solutions were known. However, the conditional version of this problem was open. In this paper, we determine the conditional matching preclusion for (n,k)-star graphs as well as classify the corresponding optimal solutions via several new results. In addition, an alternate proof of the results on the matching preclusion problem will also be given.

31

Akin, Sumeyra. "Matching with floor constraints." Theoretical Economics 16, no. 3 (2021): 911–42. http://dx.doi.org/10.3982/te3785.

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Floor constraints are a prominent feature of many matching markets, such as medical residency, teacher assignment, and military cadet matching. We develop a theory of matching markets under floor constraints. We introduce a stability notion, which we call floor respecting stability, for markets in which (hard) floor constraints must be respected. A matching is floor respecting stable if there is no coalition of doctors and hospitals that can propose an alternative matching that is feasible and an improvement for its members. Our stability notion imposes the additional condition that a coalition cannot reassign a doctor outside the coalition to another hospital (although she can be fired). This condition is necessary to guarantee the existence of stable matchings. We provide a mechanism that is strategy‐proof for doctors and implements a floor respecting stable matching.

32

Li, Hong-Hai, and Yi-Ping Liang. "On the k-matchings of the complements of bicyclic graphs." Discrete Mathematics, Algorithms and Applications 10, no. 02 (April 2018): 1850016. http://dx.doi.org/10.1142/s1793830918500167.

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A matching of a graph [Formula: see text] is a set of pairwise nonadjacent edges of [Formula: see text], and a [Formula: see text]-matching is a matching consisting of [Formula: see text] edges. In this paper, we characterize the bicyclic graphs whose complements have the extremal number of [Formula: see text]-matchings for all [Formula: see text].

33

Amir, Amihood, Eran Chencinski, Costas Iliopoulos, Tsvi Kopelowitz, and Hui Zhang. "Property matching and weighted matching." Theoretical Computer Science 395, no. 2-3 (May 2008): 298–310. http://dx.doi.org/10.1016/j.tcs.2008.01.006.

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34

Chen, Jiehua, Piotr Skowron, and Manuel Sorge. "Matchings under Preferences: Strength of Stability and Tradeoffs." ACM Transactions on Economics and Computation 9, no. 4 (December 31, 2021): 1–55. http://dx.doi.org/10.1145/3485000.

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We propose two solution concepts for matchings under preferences: robustness and near stability . The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative; together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of tradeoffs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined tradeoffs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching (if it exists), and we prove that finding a socially optimal and nearly stable matching is computationally hard.

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Huang, Chao. "Stable matching: An integer programming approach." Theoretical Economics 18, no. 1 (2023): 37–63. http://dx.doi.org/10.3982/te4830.

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This paper develops an integer programming approach to two‐sided many‐to‐one matching by investigating stable integral matchings of a fictitious market where each worker is divisible. We show that a stable matching exists in a discrete matching market when the firms' preference profile satisfies a total unimodularity condition that is compatible with various forms of complementarities. We provide a class of firms' preference profiles that satisfy this condition.

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Nguyen, Thành, and Rakesh Vohra. "Near-Feasible Stable Matchings with Couples." American Economic Review 108, no. 11 (November 1, 2018): 3154–69. http://dx.doi.org/10.1257/aer.20141188.

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The National Resident Matching program seeks a stable matching of medical students to teaching hospitals. With couples, stable matchings need not exist. Nevertheless, for any student preferences, we show that each instance of a matching problem has a “nearby” instance with a stable matching. The nearby instance is obtained by perturbing the capacities of the hospitals. In this perturbation, aggregate capacity is never reduced and can increase by at most four. The capacity of each hospital never changes by more than two. (JEL C78, D47, I11, J41, J44)

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WANG, XIUMEI, WEIPING SHANG, YIXUN LIN, and MARCELO H. CARVALHO. "A CHARACTERIZATION OF PM-COMPACT CLAW-FREE CUBIC GRAPHS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450025. http://dx.doi.org/10.1142/s1793830914500256.

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The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. This paper characterizes claw-free cubic graphs whose 1-skeleton graphs of perfect matching polytopes have diameter 1.

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Gong, Luozhong, and Weijun Liu. "The Ordering of the Unicyclic Graphs with respect to Largest Matching Root with Given Matching Number." Journal of Mathematics 2022 (May 28, 2022): 1–8. http://dx.doi.org/10.1155/2022/3589448.

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The matching roots of a simple connected graph G are the roots of the matching polynomial which is defined as M G x = ∑ k = 0 n / 2 − 1 k m G , k x n − 2 k , where m G , k is the number of the k matchings of G . Let λ 1 G denote the largest matching root of the graph G . In this paper, among the unicyclic graphs of order n , we present the ordering of the unicyclic graphs with matching number 2 according to the λ 1 G values for n ≥ 11 and also determine the graphs with the first and second largest λ 1 G values with matching number 3.

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Mazón, José Manuel, Julio Daniel Rossi, and Julián Toledo. "On optimal matching measures for matching problems related to the Euclidean distance." Mathematica Bohemica 139, no. 4 (2014): 553–66. http://dx.doi.org/10.21136/mb.2014.144132.

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40

Han, Jie. "Perfect Matchings in Hypergraphs and the Erdös Matching Conjecture." SIAM Journal on Discrete Mathematics 30, no. 3 (January 2016): 1351–57. http://dx.doi.org/10.1137/16m1056079.

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41

Kotlar, Daniel, and Ran Ziv. "Large matchings in bipartite graphs have a rainbow matching." European Journal of Combinatorics 38 (May 2014): 97–101. http://dx.doi.org/10.1016/j.ejc.2013.11.011.

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42

Aliabadi, Mohsen, Majid Hadian, and Amir Jafari. "On matching property for groups and field extensions." Journal of Algebra and Its Applications 15, no. 01 (September 7, 2015): 1650011. http://dx.doi.org/10.1142/s0219498816500110.

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In this paper we prove a sufficient condition for the existence of matchings in arbitrary groups and its linear analogue, which lead to some generalizations of the existing results in the theory of matchings in groups and central extensions of division rings. We introduce the notion of relative matchings between arrays of elements in groups and use this notion to study the behavior of matchable sets under group homomorphisms. We also present infinite families of prime numbers p such that ℤ/pℤ does not have the acyclic matching property. Finally, we introduce the linear version of acyclic matching property and show that purely transcendental field extensions satisfy this property.

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LI, YALAN, CHENGFU YE, MIAOLIN WU, and PING HAN. "Fractional Matching Preclusion for Möbius Cubes." Journal of Interconnection Networks 19, no. 04 (December 2019): 1950007. http://dx.doi.org/10.1142/s0219265919500075.

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Let F be an edge subset and F′ a subset of vertices and edges of a graph G. If G − F and G − F′ have no fractional perfect matchings, then F is a fractional matching preclusion (FMP) set and F′ is a fractional strong matching preclusion (FSMP) set of G. The FMP (FSMP) number of G is the minimum size of FMP (FSMP) sets of G. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the Möbius cube MQn. In adddition, all the optimal fractional strong preclusion sets of these graphs are categorized.

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Movahedi, Fateme. "Matching polynomials for some nanostar dendrimers." Asian-European Journal of Mathematics 14, no. 10 (March 6, 2021): 2150188. http://dx.doi.org/10.1142/s1793557121501886.

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Dendrimers are highly branched monodisperse, macromolecules and are considered in nanotechnology with a variety of suitable applications. In this paper, the matching polynomial and some results of the matchings for three classes of nanostar dendrimers are obtained. Furthermore, we express the recursive formulas of the Hosoya index for these structures of dendrimers by their matching polynomials.

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Wise, A. J. "Matching." Journal of the Institute of Actuaries 116, no. 3 (December 1989): 529–35. http://dx.doi.org/10.1017/s0020268100036684.

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1.1 The basic task of actuarial valuation is to compare the quantity of assets with the quantity of liabilities. A refinement is to compare qualities as well as quantities.1.2 The qualities of assets and liabilities are their characteristics of cash flow, duration, growth, price volatility, etc. This note considers a conceptual and mathematical framework for matching in the most general terms.1.3 Insurance work in the United Kingdom uses the notion of reserves for mismatching. Pension fund valuations in the U.K. also tend to use a notion of matching when considering the actuarial value placed on the fund.

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Sedgwick, P. "Matching." BMJ 339, no. 11 2 (November 11, 2009): b4581. http://dx.doi.org/10.1136/bmj.b4581.

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47

Costanza, M. C. "Matching." Preventive Medicine 24, no. 5 (September 1995): 425–33. http://dx.doi.org/10.1006/pmed.1995.1069.

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48

Chambers, Christopher P., and Federico Echenique. "The Core Matchings of Markets with Transfers." American Economic Journal: Microeconomics 7, no. 1 (February 1, 2015): 144–64. http://dx.doi.org/10.1257/mic.20130089.

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We characterize the structure of the set of core matchings of an assignment game (a two-sided market with transfers). Such a set satisfies a property we call consistency. Consistency of a set of matchings states that, for any matching ν, if, for each agent i there exists a matching μ in the set for which μ there μ(i) = ν (i), then ν is in the set. A set of matchings satisfies consistency if and only if there is an assignment game for which all elements of the set maximize the surplus. (JEL C78)

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Lovász, László. "Matching structure and the matching lattice." Journal of Combinatorial Theory, Series B 43, no. 2 (October 1987): 187–222. http://dx.doi.org/10.1016/0095-8956(87)90021-9.

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50

ISSIKI, Akihiro, Shuji SEO, and shigeharu MIYATA. "Stratified Image Matching Using Template Matching." Proceedings of Conference of Chugoku-Shikoku Branch 2004.42 (2004): 433–34. http://dx.doi.org/10.1299/jsmecs.2004.42.433.

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