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Journal articles on the topic 'Subcubic graph'

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Published: 7 July 2024

Last updated: 7 July 2024

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1

SKULRATTANAKULCHAI, SAN, and HAROLD N. GABOW. "COLORING ALGORITHMS ON SUBCUBIC GRAPHS." International Journal of Foundations of Computer Science 15, no. 01 (February 2004): 21–40. http://dx.doi.org/10.1142/s0129054104002285.

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We present efficient algorithms for three coloring problems on subcubic graphs. (A subcubic graph has maximum degree at most three.) The first algorithm is for 4-edge coloring, or more generally, 4-list-edge coloring. Our algorithm runs in linear time, and appears to be simpler than previous ones. The second algorithm is the first randomized EREW PRAM algorithm for the same problem. It uses O(n/ log n) processors and runs in O( log n) time with high probability, where n is the number of vertices of the graph. The third algorithm is the first linear-time algorithm to 5-total-color subcubic graphs. The fourth algorithm generalizes this to get the first linear-time algorithm to 5-list-total-color subcubic graphs. Our sequential algorithms are based on a method of ordering the vertices and edges by traversing a spanning tree of a graph in a bottom-up fashion. Our parallel algorithm is based on a simple decomposition principle for subcubic graphs.

2

Hou, Yaoping, and Dijian Wang. "Laplacian integral subcubic signed graphs." Electronic Journal of Linear Algebra 37 (February 26, 2021): 163–76. http://dx.doi.org/10.13001/ela.2021.5699.

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A (signed) graph is called Laplacian integral if all eigenvalues of its Laplacian matrix are integers. In this paper, we determine all connected Laplacian integral signed graphs of maximum degree 3; among these signed graphs,there are two classes of Laplacian integral signed graphs, one contains 4 infinite families of signed graphs and another contains 29 individual signed graphs.

3

Ma, Hongping, Zhengke Miao, Hong Zhu, Jianhua Zhang, and Rong Luo. "Strong List Edge Coloring of Subcubic Graphs." Mathematical Problems in Engineering 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/316501.

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We study strong list edge coloring of subcubic graphs, and we prove that every subcubic graph with maximum average degree less than 15/7, 27/11, 13/5, and 36/13 can be strongly list edge colored with six, seven, eight, and nine colors, respectively.

4

Wang, Fang, and Xiaoping Liu. "Coloring 3-power of 3-subdivision of subcubic graph." Discrete Mathematics, Algorithms and Applications 10, no. 03 (June 2018): 1850041. http://dx.doi.org/10.1142/s1793830918500416.

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Let [Formula: see text] be a graph and [Formula: see text] be a positive integer. The [Formula: see text]-subdivision [Formula: see text] of [Formula: see text] is the graph obtained from [Formula: see text] by replacing each edge by a path of length [Formula: see text]. The [Formula: see text]-power [Formula: see text] of [Formula: see text] is the graph with vertex set [Formula: see text] in which two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if the distance [Formula: see text] between [Formula: see text] and [Formula: see text] in [Formula: see text] is at most [Formula: see text]. Note that [Formula: see text] is the total graph [Formula: see text] of [Formula: see text]. The chromatic number [Formula: see text] of [Formula: see text] is the minimum integer [Formula: see text] for which [Formula: see text] has a proper [Formula: see text]-coloring. The total chromatic number of [Formula: see text], denoted by [Formula: see text], is the chromatic number of [Formula: see text]. Rosenfeld [On the total coloring of certain graphs, Israel J. Math. 9 (1971) 396–402] and independently, Vijayaditya [On total chromatic number of a graph, J. London Math. Soc. 2 (1971) 405–408] showed that for a subcubic graph [Formula: see text], [Formula: see text]. In this note, we prove that for a subcubic graph [Formula: see text], [Formula: see text].

5

MOHAR, BOJAN. "Median Eigenvalues of Bipartite Subcubic Graphs." Combinatorics, Probability and Computing 25, no. 5 (June 21, 2016): 768–90. http://dx.doi.org/10.1017/s0963548316000201.

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It is proved that the median eigenvalues of every connected bipartite graph G of maximum degree at most three belong to the interval [−1, 1] with a single exception of the Heawood graph, whose median eigenvalues are $\pm\sqrt{2}$. Moreover, if G is not isomorphic to the Heawood graph, then a positive fraction of its median eigenvalues lie in the interval [−1, 1]. This surprising result has been motivated by the problem about HOMO-LUMO separation that arises in mathematical chemistry.

6

Bu, Yuehua, and Hongguo Zhu. "Strong edge-coloring of subcubic planar graphs." Discrete Mathematics, Algorithms and Applications 09, no. 01 (February 2017): 1750013. http://dx.doi.org/10.1142/s1793830917500136.

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A strong[Formula: see text]-edge-coloring of a graph [Formula: see text] is a mapping [Formula: see text]: [Formula: see text], such that [Formula: see text] for every pair of distinct edges at distance at most two. The strong chromatical index of a graph [Formula: see text] is the least integer [Formula: see text] such that [Formula: see text] has a strong-[Formula: see text]-edge-coloring, denoted by [Formula: see text]. In this paper, we prove [Formula: see text] for any subcubic planar graph with [Formula: see text] and [Formula: see text]-cycles are not adjacent to [Formula: see text]-cycles.

7

Cranston, Daniel W., and Seog-Jin Kim. "List-coloring the square of a subcubic graph." Journal of Graph Theory 57, no. 1 (2007): 65–87. http://dx.doi.org/10.1002/jgt.20273.

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8

HE, Zhengyue, Li LIANG, and Wei GAO. "Two-distance vertex-distinguishing total coloring of subcubic graphs." Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science 24, no. 2 (June 28, 2023): 113–20. http://dx.doi.org/10.59277/pra-ser.a.24.2.02.

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A 2-distance vertex-distinguishing total coloring of graph G is a proper total coloring of G such that any pair of vertices at distance of two have distinct sets of colors. The 2-distance vertex-distinguishing total chromatic number $\chi_{d2}^{''}(G)$ of G is the minimum number of colors needed for a 2-distance vertex-distinguishing total coloring of G. In this paper, it's proved that if G is a subcubic graph, then $\chi_{d2}^{''}(G)\le 7$.

9

Woodall, Douglas R. "The average degree of a subcubic edge‐chromatic critical graph." Journal of Graph Theory 91, no. 2 (November 29, 2018): 103–21. http://dx.doi.org/10.1002/jgt.22423.

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10

Little, C. H. C., and F. Rendl. "Operations preserving the pfaffian property of a graph." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 2 (April 1991): 248–57. http://dx.doi.org/10.1017/s1446788700032730.

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AbstractPfaffian graphs are those which can be oriented so that the 1-factors have equal sign, as calculated according to the prescription of Kasteleyn. We consider various operations on graphs and examine their effect on the Pfaffian property. We show that the study of Pfaffian graphs may be reduced to the case of subcubic graphs (graphs in which no vertex has degree greater than 3) or bricks (3-connected bicritical graphs).

11

Gharibyan, Aram H., and Petros A. Petrosyan. "ON LOCALLY-BALANCED 2-PARTITIONS OF BIPARTITE GRAPHS." Proceedings of the YSU A: Physical and Mathematical Sciences 54, no. 3 (253) (December 15, 2020): 137–45. http://dx.doi.org/10.46991/pysu:a/2020.54.3.137.

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A \emph{$2$-partition of a graph $G$} is a function $f:V(G)\rightarrow \{0,1\}$. A $2$-partition $f$ of a graph $G$ is a \emph{locally-balanced with an open neighborhood}, if for every $v\in V(G)$, $\left\vert \vert \{u\in N_{G}(v)\colon\,f(u)=0\}\vert - \vert \{u\in N_{G}(v)\colon\,f(u)=1\}\vert \right\vert\leq 1$. A bipartite graph is \emph{$(a,b)$-biregular} if all vertices in one part have degree $a$ and all vertices in the other part have degree $b$. In this paper we prove that the problem of deciding, if a given graph has a locally-balanced $2$-partition with an open neighborhood is $NP$-complete even for $(3,8)$-biregular bipartite graphs. We also prove that a $(2,2k+1)$-biregular bipartite graph has a locally-balanced $2$-partition with an open neighbourhood if and only if it has no cycle of length $2 \pmod{4}$. Next, we prove that if $G$ is a subcubic bipartite graph that has no cycle of length $2 \pmod{4}$, then $G$ has a locally-balanced $2$-partition with an open neighbourhood. Finally, we show that all doubly convex bipartite graphs have a locally-balanced $2$-partition with an open neighbourhood.

12

Chen, Lily, and Yanyi Li. "A New Proof for a Result on the Inclusion Chromatic Index of Subcubic Graphs." Axioms 11, no. 1 (January 17, 2022): 33. http://dx.doi.org/10.3390/axioms11010033.

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Let G be a graph with a minimum degree δ of at least two. The inclusion chromatic index of G, denoted by χ⊂′(G), is the minimum number of colors needed to properly color the edges of G so that the set of colors incident with any vertex is not contained in the set of colors incident to any of its neighbors. We prove that every connected subcubic graph G with δ(G)≥2 either has an inclusion chromatic index of at most six, or G is isomorphic to K^2,3, where its inclusion chromatic index is seven.

13

Bueno, Letícia R., Lucia D. Penso, Fábio Protti, Victor R. Ramos, Dieter Rautenbach, and Uéverton S. Souza. "On the hardness of finding the geodetic number of a subcubic graph." Information Processing Letters 135 (July 2018): 22–27. http://dx.doi.org/10.1016/j.ipl.2018.02.012.

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14

Khoeilar, R., H. Karami, M. Chellali, S. M. Sheikholeslami, and L. Volkmann. "A proof of a conjecture on the differential of a subcubic graph." Discrete Applied Mathematics 287 (December 2020): 27–39. http://dx.doi.org/10.1016/j.dam.2020.07.018.

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15

Feghali, Carl, and Robert Šámal. "Decomposing a triangle-free planar graph into a forest and a subcubic forest." European Journal of Combinatorics 116 (February 2024): 103878. http://dx.doi.org/10.1016/j.ejc.2023.103878.

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16

Kim, Seog-Jin, and Xiaopan Lian. "The square of every subcubic planar graph of girth at least 6 is 7-choosable." Discrete Mathematics 347, no. 6 (June 2024): 113963. http://dx.doi.org/10.1016/j.disc.2024.113963.

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17

Lei, Yuxiang, Yulei Sui, Shin Hwei Tan, and Qirun Zhang. "Recursive State Machine Guided Graph Folding for Context-Free Language Reachability." Proceedings of the ACM on Programming Languages 7, PLDI (June 6, 2023): 318–42. http://dx.doi.org/10.1145/3591233.

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Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

18

JOHNSON, J. ROBERT, and KLAS MARKSTRÖM. "Turán and Ramsey Properties of Subcube Intersection Graphs." Combinatorics, Probability and Computing 22, no. 1 (October 3, 2012): 55–70. http://dx.doi.org/10.1017/s0963548312000429.

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The discrete cube {0, 1}d is a fundamental combinatorial structure. A subcube of {0, 1}d is a subset of 2k of its points formed by fixing k coordinates and allowing the remaining d − k to vary freely. This paper is concerned with patterns of intersections among subcubes of the discrete cube. Two sample questions along these lines are as follows: given a family of subcubes in which no r + 1 of them have non-empty intersection, how many pairwise intersections can we have? How many subcubes can we have if among them there are no k which have non-empty intersection and no l which are pairwise disjoint?These questions are naturally expressed using intersection graphs. The intersection graph of a family of sets has one vertex for each set in the family with two vertices being adjacent if the corresponding subsets intersect. Let $\I(n,d)$ be the set of all n vertex graphs which can be represented as the intersection graphs of subcubes in {0, 1}d. With this notation our first question above asks for the largest number of edges in a Kr+1-free graph in $\I(n,d)$. As such it is a Turán-type problem. We answer this question asymptotically for some ranges of r and d. More precisely we show that if $(k+1)2^{\lfloor\frac{d}{k+1}\rfloor}<n\leq k2^{\lfloor\frac{d}{k}\rfloor}$ for some integer k ≥ 2 then the maximum edge density is $\bigl(1-\frac{1}{k}-o(1)\bigr)$ provided that n is not too close to the lower limit of the range.The second question can be thought of as a Ramsey-type problem. The maximum such n can be defined in the same way as the usual Ramsey number but only considering graphs which are in $\I(n,d)$. We give bounds for this maximum n mainly concentrating on the case that l is fixed, and make some comparisons with the usual Ramsey number.

19

Wang, Dijian, and Yaoping Hou. "Integral signed subcubic graphs." Linear Algebra and its Applications 593 (May 2020): 29–44. http://dx.doi.org/10.1016/j.laa.2020.01.037.

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20

Bessy, Stéphane, Johannes Pardey, and Dieter Rautenbach. "Exponential independence in subcubic graphs." Discrete Mathematics 344, no. 8 (August 2021): 112439. http://dx.doi.org/10.1016/j.disc.2021.112439.

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21

Karthick, T., and C. R. Subramanian. "Star coloring of subcubic graphs." Discussiones Mathematicae Graph Theory 33, no. 2 (2013): 373. http://dx.doi.org/10.7151/dmgt.1672.

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22

Joos, Felix, Dieter Rautenbach, and Thomas Sasse. "Induced Matchings in Subcubic Graphs." SIAM Journal on Discrete Mathematics 28, no. 1 (January 2014): 468–73. http://dx.doi.org/10.1137/130944424.

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23

Skulrattanakulchai, San. "Acyclic colorings of subcubic graphs." Information Processing Letters 92, no. 4 (November 2004): 161–67. http://dx.doi.org/10.1016/j.ipl.2004.08.002.

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24

Liu, Chun-Hung, and Gexin Yu. "Linear colorings of subcubic graphs." European Journal of Combinatorics 34, no. 6 (August 2013): 1040–50. http://dx.doi.org/10.1016/j.ejc.2013.02.008.

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25

ANGELES-CANUL, RICARDO JAVIER, RACHAEL M. NORTON, MICHAEL C. OPPERMAN, CHRISTOPHER C. PARIBELLO, MATTHEW C. RUSSELL, and CHRISTINO TAMON. "QUANTUM PERFECT STATE TRANSFER ON WEIGHTED JOIN GRAPHS." International Journal of Quantum Information 07, no. 08 (December 2009): 1429–45. http://dx.doi.org/10.1142/s0219749909006103.

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This paper studies quantum perfect state transfer on weighted graphs. We prove that the join of a weighted two-vertex graph with any regular graph has perfect state transfer. This generalizes a result of Casaccino et al.1 where the regular graph is a complete graph with or without a missing edge. In contrast, we prove that the half-join of a weighted two-vertex graph with any weighted regular graph has no perfect state transfer. As a corollary, unlike for complete graphs, adding weights in complete bipartite graphs does not produce perfect state transfer. We also observe that any Hamming graph has perfect state transfer between each pair of its vertices. The result is a corollary of a closure property on weighted Cartesian products of perfect state transfer graphs. Moreover, on a hypercube, we show that perfect state transfer occurs between uniform superpositions on pairs of arbitrary subcubes, thus generalizing results of Bernasconi et al.2 and Moore and Russell.3

26

Munaro, Andrea. "On line graphs of subcubic triangle-free graphs." Discrete Mathematics 340, no. 6 (June 2017): 1210–26. http://dx.doi.org/10.1016/j.disc.2017.01.006.

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27

Pradeep, Kavita, and V. Vijayalakshmi. "Star Edge Coloring of Subcubic Graphs." Applied Mathematics & Information Sciences 13, no. 2 (March 1, 2019): 279–84. http://dx.doi.org/10.18576/amis/130216.

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28

Małafiejska, Anna, and Michał Małafiejski. "Interval incidence coloring of subcubic graphs." Discussiones Mathematicae Graph Theory 37, no. 2 (2017): 427. http://dx.doi.org/10.7151/dmgt.1962.

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29

Atanasov, Risto, Mirko Petruševski, and Riste Škrekovski. "Odd edge-colorability of subcubic graphs." Ars Mathematica Contemporanea 10, no. 2 (March 1, 2016): 359–70. http://dx.doi.org/10.26493/1855-3974.957.97c.

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30

Wigal, Michael C., Youngho Yoo, and Xingxing Yu. "Approximating TSP walks in subcubic graphs." Journal of Combinatorial Theory, Series B 158 (January 2023): 70–104. http://dx.doi.org/10.1016/j.jctb.2022.09.002.

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31

Kang, Ross J., Matthias Mnich, and Tobias Müller. "Induced Matchings in Subcubic Planar Graphs." SIAM Journal on Discrete Mathematics 26, no. 3 (January 2012): 1383–411. http://dx.doi.org/10.1137/100808824.

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32

Chen, Min, and André Raspaud. "Acyclic improper choosability of subcubic graphs." Applied Mathematics and Computation 356 (September 2019): 92–98. http://dx.doi.org/10.1016/j.amc.2019.03.027.

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33

Zhang, Xin. "Equitable vertex arboricity of subcubic graphs." Discrete Mathematics 339, no. 6 (June 2016): 1724–26. http://dx.doi.org/10.1016/j.disc.2016.02.003.

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34

Basavaraju, Manu, and L. Sunil Chandran. "Acyclic edge coloring of subcubic graphs." Discrete Mathematics 308, no. 24 (December 2008): 6650–53. http://dx.doi.org/10.1016/j.disc.2007.12.036.

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35

Kavita Pradeep and V Vijayalakshmi. "Star Chromatic Index of Subcubic Graphs." Electronic Notes in Discrete Mathematics 53 (September 2016): 155–64. http://dx.doi.org/10.1016/j.endm.2016.05.014.

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36

Brešar, Boštjan, Nicolas Gastineau, and Olivier Togni. "Packing colorings of subcubic outerplanar graphs." Aequationes mathematicae 94, no. 5 (April 28, 2020): 945–67. http://dx.doi.org/10.1007/s00010-020-00721-6.

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37

Hocquard, Hervé, and Petru Valicov. "Strong edge colouring of subcubic graphs." Discrete Applied Mathematics 159, no. 15 (September 2011): 1650–57. http://dx.doi.org/10.1016/j.dam.2011.06.015.

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38

Gui, Hao, Weifan Wang, Yiqiao Wang, and Zhao Zhang. "Equitable total-coloring of subcubic graphs." Discrete Applied Mathematics 184 (March 2015): 167–70. http://dx.doi.org/10.1016/j.dam.2014.11.014.

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39

Fürst, Maximilian, Michael A. Henning, and Dieter Rautenbach. "Uniquely restricted matchings in subcubic graphs." Discrete Applied Mathematics 262 (June 2019): 189–94. http://dx.doi.org/10.1016/j.dam.2019.02.013.

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40

Chen, Min, André Raspaud, and Weifan Wang. "6-Star-Coloring of Subcubic Graphs." Journal of Graph Theory 72, no. 2 (June 1, 2012): 128–45. http://dx.doi.org/10.1002/jgt.21636.

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41

Aboulker, Pierre, Marko Radovanović, Nicolas Trotignon, Théophile Trunck, and Kristina Vušković. "Linear Balanceable and Subcubic Balanceable Graphs*." Journal of Graph Theory 75, no. 2 (February 14, 2013): 150–66. http://dx.doi.org/10.1002/jgt.21728.

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42

Foucaud, Florent, Hervé Hocquard, Suchismita Mishra, Narayanan Narayanan, Reza Naserasr, Éric Sopena, and Petru Valicov. "Exact square coloring of subcubic planar graphs." Discrete Applied Mathematics 293 (April 2021): 74–89. http://dx.doi.org/10.1016/j.dam.2021.01.007.

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43

Kerdjoudj, Samia, Alexander V. Kostochka, and André Raspaud. "List star edge-coloring of subcubic graphs." Discussiones Mathematicae Graph Theory 38, no. 4 (2018): 1037. http://dx.doi.org/10.7151/dmgt.2037.

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44

Kostochka, Alexandr, and Xujun Liu. "Packing (1,1,2,4)-coloring of subcubic outerplanar graphs." Discrete Applied Mathematics 302 (October 2021): 8–15. http://dx.doi.org/10.1016/j.dam.2021.05.031.

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45

Lv, Jian-Bo, Jianxi Li, and Nian Hong Zhou. "List injective edge-coloring of subcubic graphs." Discrete Applied Mathematics 302 (October 2021): 163–70. http://dx.doi.org/10.1016/j.dam.2021.07.010.

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46

Dvořák, Zdeněk, Riste Škrekovski, and Martin Tancer. "List-Coloring Squares of Sparse Subcubic Graphs." SIAM Journal on Discrete Mathematics 22, no. 1 (January 2008): 139–59. http://dx.doi.org/10.1137/050634049.

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47

Huo, Jingjing, Weifan Wang, and Chuandong Xu. "Neighbor Sum Distinguishing Index of Subcubic Graphs." Graphs and Combinatorics 33, no. 2 (January 7, 2017): 419–31. http://dx.doi.org/10.1007/s00373-017-1760-0.

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48

Gu, Jing, Weifan Wang, Yiqiao Wang, and Ying Wang. "Strict Neighbor-Distinguishing Index of Subcubic Graphs." Graphs and Combinatorics 37, no. 1 (November 9, 2020): 355–68. http://dx.doi.org/10.1007/s00373-020-02246-w.

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49

Juvan, Martin, Bojan Mohar, and Riste Sˇkrekovski. "On list edge-colorings of subcubic graphs." Discrete Mathematics 187, no. 1-3 (June 1998): 137–49. http://dx.doi.org/10.1016/s0012-365x(97)00230-6.

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50

Zhu, Xuding. "Bipartite density of triangle-free subcubic graphs." Discrete Applied Mathematics 157, no. 4 (February 2009): 710–14. http://dx.doi.org/10.1016/j.dam.2008.07.007.

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