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Journal articles on the topic 'Contraction perfect graphs'

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Author: Grafiati
Published: 24 August 2024

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1

Diner, Öznur Yaşar, Daniël Paulusma, Christophe Picouleau, and Bernard Ries. "Contraction and deletion blockers for perfect graphs and H-free graphs." Theoretical Computer Science 746 (October 2018): 49–72. http://dx.doi.org/10.1016/j.tcs.2018.06.023.

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2

Bertschi, Marc E. "Perfectly contractile graphs." Journal of Combinatorial Theory, Series B 50, no. 2 (December 1990): 222–30. http://dx.doi.org/10.1016/0095-8956(90)90077-d.

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3

Maffray, Frédéric, and Nicolas Trotignon. "Algorithms for Perfectly Contractile Graphs." SIAM Journal on Discrete Mathematics 19, no. 3 (January 2005): 553–74. http://dx.doi.org/10.1137/s0895480104442522.

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4

Sales, Cláudia Linhares, Frédéric Maffray, and Bruce Reed. "On Planar Perfectly Contractile Graphs." Graphs and Combinatorics 13, no. 2 (June 1997): 167–87. http://dx.doi.org/10.1007/bf03352994.

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5

Rusu, Irena. "Perfectly contractile diamond-free graphs." Journal of Graph Theory 32, no. 4 (December 1999): 359–89. http://dx.doi.org/10.1002/(sici)1097-0118(199912)32:4<359::aid-jgt5>3.0.co;2-u.

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6

Sales, Cláudia Linhares, and Frédéric Maffray. "On dart-free perfectly contractile graphs." Theoretical Computer Science 321, no. 2-3 (August 2004): 171–94. http://dx.doi.org/10.1016/j.tcs.2003.11.026.

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7

Lévêque, Benjamin, and Frédéric Maffray. "Coloring Bull-Free Perfectly Contractile Graphs." SIAM Journal on Discrete Mathematics 21, no. 4 (January 2008): 999–1018. http://dx.doi.org/10.1137/06065948x.

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8

Maffray, Frédéric, and Nicolas Trotignon. "A class of perfectly contractile graphs." Journal of Combinatorial Theory, Series B 96, no. 1 (January 2006): 1–19. http://dx.doi.org/10.1016/j.jctb.2005.06.011.

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9

PANDA, SWARUP. "Inverses of bicyclic graphs." Electronic Journal of Linear Algebra 32 (February 6, 2017): 217–31. http://dx.doi.org/10.13001/1081-3810.3322.

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A graph G is said to be nonsingular (resp., singular) if its adjacency matrix A(G) is nonsingular (resp., singular). The inverse of a nonsingular graph G is the unique weighted graph whose adjacency matrix is similar to the inverse of the adjacency matrix A(G) via a diagonal matrix of ±1s. Consider connected bipartite graphs with unique perfect matchings such that the graph obtained by contracting all matching edges is also bipartite. In [C.D. Godsil. Inverses of trees. Combinatorica, 5(1):33–39, 1985.], Godsil proved that such graphs are invertible. He posed the question of characterizing the bipartite graphs with unique perfect matchings possessing inverses. In this article, Godsil’s question for the class of bicyclic graphs is answered.
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10

Fischer, Ilse, and C. H. C. Little. "Even Circuits of Prescribed Clockwise Parity." Electronic Journal of Combinatorics 10, no. 1 (November 24, 2003). http://dx.doi.org/10.37236/1738.

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We show that a graph has an orientation under which every circuit of even length is clockwise odd if and only if the graph contains no subgraph which is, after the contraction of at most one circuit of odd length, an even subdivision of $K_{2,3}$. In fact we give a more general characterisation of graphs that have an orientation under which every even circuit has a prescribed clockwise parity. Moreover we show that this characterisation has an equivalent analogue for signed graphs. We were motivated to study the original problem by our work on Pfaffian graphs, which are the graphs that have an orientation under which every alternating circuit is clockwise odd. Their significance is that they are precisely the graphs to which Kasteleyn's powerful method for enumerating perfect matchings may be applied.
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11

Li, Zhongyang. "Limit Shape of Perfect Matchings on Contracting Bipartite Graphs." International Mathematics Research Notices, March 10, 2021. http://dx.doi.org/10.1093/imrn/rnab005.

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Abstract We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling limit. The results can also be applied to prove the existence of multiple disconnected liquid regions for all the contracting square-hexagon lattices with certain edge weights, extending the results proved in [ 13] for contracting square-hexagon lattices where the number of square rows in each period is either 0 or 1.
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12

Bachtler, Oliver, and Sven O. Krumke. "Towards Obtaining a 3-Decomposition From a Perfect Matching." Electronic Journal of Combinatorics 29, no. 4 (November 4, 2022). http://dx.doi.org/10.37236/11128.

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A decomposition of a graph is a set of subgraphs whose edges partition those of $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph, and a matching. It has been settled for special classes of graphs, one of the first results being for Hamiltonian graphs. In the past two years several new results have been obtained, adding the classes of plane, claw-free, and 3-connected tree-width 3 graphs to the list. In this paper, we regard a natural extension of Hamiltonian graphs: removing a Hamiltonian cycle from a cubic graph leaves a perfect matching. Conversely, removing a perfect matching $M$ from a cubic graph $G$ leaves a disjoint union of cycles. Contracting these cycles yields a new graph $G_M$. The graph $G$ is star-like if $G_M$ is a star for some perfect matching $M$, making Hamiltonian graphs star-like. We extend the technique used to prove that Hamiltonian graphs satisfy the 3-decomposition conjecture to show that 3-connected star-like graphs satisfy it as well.
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13

SALES, C. "On dart-free perfectly contractile graphs*1." Theoretical Computer Science, May 2004. http://dx.doi.org/10.1016/s0304-3975(03)00645-5.

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14

Ohsugi, Hidefumi, Kazuki Shibata, and Akiyoshi Tsuchiya. "Perfectly contractile graphs and quadratic toric rings." Bulletin of the London Mathematical Society, December 29, 2022. http://dx.doi.org/10.1112/blms.12789.

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15

Nurlaelah, Nurlaelah, Basit Al Hanif, and Otti Ilham Khair. "Application of Islamic Religious Values on Construction Workers (Case Study: Pt. Alcos Graha Jaya)." Engineering and Technology Journal 09, no. 07 (July 25, 2024). http://dx.doi.org/10.47191/etj/v9i07.12.

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Workers in a construction company are a very important element for the whole company. Therefore, the presence of workers who have high enthusiasm and outstanding achievements in their fields is very important, so that they can create optimal performance. Workers who are able to provide good performance will have a positive impact and produce high-quality work. To achieve this goal, there are several factors that support, one of which is applying religious values, especially in the Islamic context to construction work. By using the questionnaire method given to construction workers at PT ALCOS GRAHA JAYA, regression results were obtained with a t value of 11.290 greater than t table 2.00958, while the correlation result is 0.850 which means that there is a perfect correlation between the application of Islamic values and the performance of construction workers in the contractor company.
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