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Journal articles on the topic 'Chordal Bipartite Graphs'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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1

McKee, Terry A. "Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs." Discrete Mathematics 260, no. 1-3 (January 2003): 231–38. http://dx.doi.org/10.1016/s0012-365x(02)00674-x.

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2

Nguyen, Ngoc Tuy, Jörg Bornemann, and Van Bang Le. "Graph classes related to chordal graphs and chordal bipartite graphs." Electronic Notes in Discrete Mathematics 27 (October 2006): 73–74. http://dx.doi.org/10.1016/j.endm.2006.08.062.

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3

Uehara, Ryuhei, Seinosuke Toda, and Takayuki Nagoya. "Graph isomorphism completeness for chordal bipartite graphs and strongly chordal graphs." Discrete Applied Mathematics 145, no. 3 (January 2005): 479–82. http://dx.doi.org/10.1016/j.dam.2004.06.008.

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4

McKee, Terry A. "Erratum to “Chordal bipartite, strongly chordal, and strongly chordal bipartite graphs”." Discrete Mathematics 272, no. 2-3 (November 2003): 307. http://dx.doi.org/10.1016/s0012-365x(03)00254-1.

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5

Takaoka, Asahi. "Complexity of Hamiltonian Cycle Reconfiguration." Algorithms 11, no. 9 (September 17, 2018): 140. http://dx.doi.org/10.3390/a11090140.

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The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained from C i − 1 by a switch for each i with 1 ≤ i ≤ t , where a switch is the replacement of a pair of edges u v and w z on a Hamiltonian cycle with the edges u w and v z of G, given that u w and v z did not appear on the cycle. We show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete, settling an open question posed by Ito et al. (2011) and van den Heuvel (2013). More precisely, we show that the Hamiltonian cycle reconfiguration problem is PSPACE-complete for chordal bipartite graphs, strongly chordal split graphs, and bipartite graphs with maximum degree 6. Bipartite permutation graphs form a proper subclass of chordal bipartite graphs, and unit interval graphs form a proper subclass of strongly chordal graphs. On the positive side, we show that, for any two Hamiltonian cycles of a bipartite permutation graph and a unit interval graph, there is a sequence of switches transforming one cycle to the other, and such a sequence can be obtained in linear time.

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6

PRADHAN, D. "COMPLEXITY OF CERTAIN FUNCTIONAL VARIANTS OF TOTAL DOMINATION IN CHORDAL BIPARTITE GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 03 (August 6, 2012): 1250045. http://dx.doi.org/10.1142/s1793830912500450.

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In this paper, we consider minimum total domination problem along with two of its variations namely, minimum signed total domination problem and minimum minus total domination problem for chordal bipartite graphs. In the minimum total domination problem, the objective is to find a smallest size subset TD ⊆ V of a given graph G = (V, E) such that |TD∩NG(v)| ≥ 1 for every v ∈ V. In the minimum signed (minus) total domination problem for a graph G = (V, E), it is required to find a function f : V → {-1, 1} ({-1, 0, 1}) such that f(NG(v)) = ∑u∈NG(v)f(u) ≥ 1 for each v ∈ V, and the cost f(V) = ∑v∈V f(v) is minimized. We first show that for a given chordal bipartite graph G = (V, E) with a weak elimination ordering, a minimum total dominating set can be computed in O(n + m) time, where n = |V| and m = |E|. This improves the complexity of the minimum total domination problem for chordal bipartite graphs from O(n2) time to O(n + m) time. We then adopt a unified approach to solve the minimum signed (minus) total domination problem for chordal bipartite graphs in O(n + m) time. The method is also able to solve the minimum k-tuple total domination problem for chordal bipartite graphs in O(n + m) time. For a fixed integer k ≥ 1 and a graph G = (V, E), the minimum k-tuple total domination problem is to find a smallest subset TDk ⊆ V such that |TDk ∩ NG(v)| ≥ k for every v ∈ V.

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7

Bouchitt�, Vincent. "Chordal bipartite graphs and crowns." Order 2, no. 2 (1985): 119–22. http://dx.doi.org/10.1007/bf00334850.

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8

Kloks, T., and D. Kratsch. "Treewidth of Chordal Bipartite Graphs." Journal of Algorithms 19, no. 2 (September 1995): 266–81. http://dx.doi.org/10.1006/jagm.1995.1037.

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9

LEE, CHUAN-MIN, and CHENG-CHIEN LO. "On the Complexity of Reverse Minus and Signed Domination on Graphs." Journal of Interconnection Networks 15, no. 01n02 (March 2015): 1550008. http://dx.doi.org/10.1142/s0219265915500085.

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Motivated by the concept of reverse signed domination, we introduce the reverse minus domination problem on graphs, and study the reverse minus and signed domination problems from the algorithmic point of view. In this paper, we show that both the reverse minus and signed domination problems are polynomial-time solvable for strongly chordal graphs and distance-hereditary graphs, and are linear-time solvable for trees. For chordal graphs and bipartite planar graphs, however, we show that the decision problem corresponding to the reverse minus domination problem is NP-complete. For doubly chordal graphs and bipartite planar graphs, we show that the decision problem corresponding to the reverse signed domination problem is NP-complete. Furthermore, we show that even when restricted to bipartite planar graphs or doubly chordal graphs, the reverse signed domination problem is not fixed parameter tractable.

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10

Bonamy, Marthe, Matthew Johnson, Ioannis Lignos, Viresh Patel, and Daniël Paulusma. "Reconfiguration graphs for vertex colourings of chordal and chordal bipartite graphs." Journal of Combinatorial Optimization 27, no. 1 (April 26, 2012): 132–43. http://dx.doi.org/10.1007/s10878-012-9490-y.

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11

Heggernes, Pinar, Federico Mancini, Charis Papadopoulos, and R. Sritharan. "Strongly chordal and chordal bipartite graphs are sandwich monotone." Journal of Combinatorial Optimization 22, no. 3 (April 23, 2010): 438–56. http://dx.doi.org/10.1007/s10878-010-9322-x.

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12

Bakonyi, Mihály, and Aaron Bono. "Several results on chordal bipartite graphs." Czechoslovak Mathematical Journal 47, no. 4 (December 1997): 577–83. http://dx.doi.org/10.1023/a:1022806215452.

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13

Chandran, L. Sunil, Mathew C. Francis, and Rogers Mathew. "Chordal Bipartite Graphs with High Boxicity." Graphs and Combinatorics 27, no. 3 (March 17, 2011): 353–62. http://dx.doi.org/10.1007/s00373-011-1017-2.

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14

Müller, Haiko. "Hamiltonian circuits in chordal bipartite graphs." Discrete Mathematics 156, no. 1-3 (September 1996): 291–98. http://dx.doi.org/10.1016/0012-365x(95)00057-4.

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15

Jobson, Adam S., André E. Kézdy, and Susan C. White. "Connected matchings in chordal bipartite graphs." Discrete Optimization 14 (November 2014): 34–45. http://dx.doi.org/10.1016/j.disopt.2014.06.003.

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16

Sritharan, R. "Chordal bipartite completion of colored graphs." Discrete Mathematics 308, no. 12 (June 2008): 2581–88. http://dx.doi.org/10.1016/j.disc.2007.06.004.

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17

Huang, Jing. "Representation characterizations of chordal bipartite graphs." Journal of Combinatorial Theory, Series B 96, no. 5 (September 2006): 673–83. http://dx.doi.org/10.1016/j.jctb.2006.01.001.

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18

Brandstädt, Andreas. "Classes of bipartite graphs related to chordal graphs." Discrete Applied Mathematics 32, no. 1 (June 1991): 51–60. http://dx.doi.org/10.1016/0166-218x(91)90023-p.

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19

Alkam, Osama, and Emad Abu Osba. "Zero Divisor Graph for the Ring of Eisenstein Integers Modulo n." Algebra 2014 (December 15, 2014): 1–6. http://dx.doi.org/10.1155/2014/146873.

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Let En be the ring of Eisenstein integers modulo n. In this paper we study the zero divisor graph Γ(En). We find the diameters and girths for such zero divisor graphs and characterize n for which the graph Γ(En) is complete, complete bipartite, bipartite, regular, Eulerian, Hamiltonian, or chordal.

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20

Cerioli, Márcia R., and Daniel F. D. Posner. "On λ-coloring split, chordal bipartite and weakly chordal graphs." Electronic Notes in Discrete Mathematics 35 (December 2009): 299–304. http://dx.doi.org/10.1016/j.endm.2009.11.049.

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21

Dragan, Feodor F. "Strongly orderable graphs A common generalization of strongly chordal and chordal bipartite graphs." Discrete Applied Mathematics 99, no. 1-3 (February 2000): 427–42. http://dx.doi.org/10.1016/s0166-218x(99)00149-3.

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22

Damaschke, Peter, Haiko Müller, and Dieter Kratsch. "Domination in convex and chordal bipartite graphs." Information Processing Letters 36, no. 5 (December 1990): 231–36. http://dx.doi.org/10.1016/0020-0190(90)90147-p.

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23

Dabrowski, Konrad, Vadim V. Lozin, and Victor Zamaraev. "On factorial properties of chordal bipartite graphs." Discrete Mathematics 312, no. 16 (August 2012): 2457–65. http://dx.doi.org/10.1016/j.disc.2012.04.010.

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24

Panda, B. S., and D. Pradhan. "A linear time algorithm to compute a minimum restrained dominating set in proper interval graphs." Discrete Mathematics, Algorithms and Applications 07, no. 02 (May 25, 2015): 1550020. http://dx.doi.org/10.1142/s1793830915500202.

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A set D ⊆ V is a restrained dominating set of a graph G = (V, E) if every vertex in V\D is adjacent to a vertex in D and a vertex in V\D. Given a graph G and a positive integer k, the restrained domination problem is to check whether G has a restrained dominating set of size at most k. The restrained domination problem is known to be NP-complete even for chordal graphs. In this paper, we propose a linear time algorithm to compute a minimum restrained dominating set of a proper interval graph. We present a polynomial time reduction that proves the NP-completeness of the restrained domination problem for undirected path graphs, chordal bipartite graphs, circle graphs, and planar graphs.

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25

Panda, B. S., and D. Pradhan. "Minimum paired-dominating set in chordal bipartite graphs and perfect elimination bipartite graphs." Journal of Combinatorial Optimization 26, no. 4 (April 10, 2012): 770–85. http://dx.doi.org/10.1007/s10878-012-9483-x.

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26

Cerioli, Márcia R., and Daniel F. D. Posner. "On L(2,1)-coloring split, chordal bipartite, and weakly chordal graphs." Discrete Applied Mathematics 160, no. 18 (December 2012): 2655–61. http://dx.doi.org/10.1016/j.dam.2012.03.018.

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27

Heggernes, Pinar, Pim van ʼt Hof, Benjamin Lévêque, and Paul Christophe. "Contracting chordal graphs and bipartite graphs to paths and trees." Electronic Notes in Discrete Mathematics 37 (August 2011): 87–92. http://dx.doi.org/10.1016/j.endm.2011.05.016.

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28

Heggernes, Pinar, Pim van ’t Hof, Benjamin Lévêque, and Christophe Paul. "Contracting chordal graphs and bipartite graphs to paths and trees." Discrete Applied Mathematics 164 (February 2014): 444–49. http://dx.doi.org/10.1016/j.dam.2013.02.025.

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29

Panda, B. S., and Shaily Verma. "On partial Grundy coloring of bipartite graphs and chordal graphs." Discrete Applied Mathematics 271 (December 2019): 171–83. http://dx.doi.org/10.1016/j.dam.2019.08.005.

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30

Ponomarenko, Ilia, and Grigory Ryabov. "The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite Claw." Graphs and Combinatorics 37, no. 3 (March 25, 2021): 1089–102. http://dx.doi.org/10.1007/s00373-021-02308-7.

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31

Berry, Anne, Andreas Brandstädt, and Konrad Engel. "The Dilworth Number of Auto-Chordal Bipartite Graphs." Graphs and Combinatorics 31, no. 5 (September 26, 2014): 1463–71. http://dx.doi.org/10.1007/s00373-014-1471-8.

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32

Artigas, D., and R. Sritharan. "Geodeticity of the contour of chordal bipartite graphs." Electronic Notes in Discrete Mathematics 50 (December 2015): 237–42. http://dx.doi.org/10.1016/j.endm.2015.07.040.

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33

Golovach, Petr A., Pinar Heggernes, Mamadou M. Kanté, Dieter Kratsch, and Yngve Villanger. "Enumerating minimal dominating sets in chordal bipartite graphs." Discrete Applied Mathematics 199 (January 2016): 30–36. http://dx.doi.org/10.1016/j.dam.2014.12.010.

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34

de Figueiredo, C. M. H., L. Faria, S. Klein, and R. Sritharan. "On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs." Theoretical Computer Science 381, no. 1-3 (August 2007): 57–67. http://dx.doi.org/10.1016/j.tcs.2007.04.007.

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35

Kamath, S. S., A. Senthil Thilak, and M. Rashmi. "Algorithmic aspects of k-part degree restricted domination in graphs." Discrete Mathematics, Algorithms and Applications 12, no. 05 (July 7, 2020): 2050057. http://dx.doi.org/10.1142/s1793830920500573.

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The concept of network is predominantly used in several applications of computer communication networks. It is also a fact that the dominating set acts as a virtual backbone in a communication network. These networks are vulnerable to breakdown due to various causes, including traffic congestion. In such an environment, it is necessary to regulate the traffic so that these vulnerabilities could be reasonably controlled. Motivated by this, [Formula: see text]-part degree restricted domination is defined as follows. For a positive integer [Formula: see text], a dominating set [Formula: see text] of a graph [Formula: see text] is said to be a [Formula: see text]-part degree restricted dominating set ([Formula: see text]-DRD set) if for all [Formula: see text], there exists a set [Formula: see text] such that [Formula: see text] and [Formula: see text]. The minimum cardinality of a [Formula: see text]-DRD set of a graph [Formula: see text] is called the [Formula: see text]-part degree restricted domination number of [Formula: see text] and is denoted by [Formula: see text]. In this paper, we present a polynomial time reduction that proves the NP -completeness of the [Formula: see text]-part degree restricted domination problem for bipartite graphs, chordal graphs, undirected path graphs, chordal bipartite graphs, circle graphs, planar graphs and split graphs. We propose a polynomial time algorithm to compute a minimum [Formula: see text]-DRD set of a tree and minimal [Formula: see text]-DRD set of a graph.

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36

YETİM, Mehmet Akif. "Independence complexes of strongly orderable graphs." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 2 (June 30, 2022): 445–55. http://dx.doi.org/10.31801/cfsuasmas.874855.

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We prove that for any finite strongly orderable (generalized strongly chordal) graph G, the independence complex Ind(G) is either contractible or homotopy equivalent to a wedge of spheres of dimension at least bp(G)−1, where bp(G) is the biclique vertex partition number of G. In particular, we show that if G is a chordal bipartite graph, then Ind(G) is either contractible or homotopy equivalent to a sphere of dimension at least bp(G) − 1.

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37

Panda, B. S., and Priyamvada. "Injective coloring of some subclasses of bipartite graphs and chordal graphs." Discrete Applied Mathematics 291 (March 2021): 68–87. http://dx.doi.org/10.1016/j.dam.2020.12.006.

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38

Lozin, V., and D. Rautenbach. "Chordal bipartite graphs of bounded tree- and clique-width." Discrete Mathematics 283, no. 1-3 (June 2004): 151–58. http://dx.doi.org/10.1016/j.disc.2004.02.008.

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39

Cohen, Elad, Martin Charles Golumbic, Marina Lipshteyn, and Michal Stern. "On the bi-enhancement of chordal-bipartite probe graphs." Information Processing Letters 110, no. 5 (February 2010): 193–97. http://dx.doi.org/10.1016/j.ipl.2009.12.003.

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40

Lin, Chih-Yuan, Jia-Jie Liu, Yue-Li Wang, William Chung-Kung Yen, and Chiun-Chieh Hsu. "The Outer-Paired Domination of Graphs." International Journal of Foundations of Computer Science 33, no. 02 (February 2022): 141–48. http://dx.doi.org/10.1142/s0129054122500034.

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In this paper, we introduce a new variant of domination called the outer-paired domination. For a graph [Formula: see text], an outer-paired dominating set [Formula: see text] is a dominating set of [Formula: see text] such that the induced subgraph of [Formula: see text] contains a perfect matching. The outer-paired domination number of a graph [Formula: see text] is the cardinality of a minimum outer-paired dominating set of [Formula: see text]. We show that finding the outer-paired domination number of a graph [Formula: see text] is NP-hard on bipartite graphs, chordal graphs, and planar graphs. We also propose a linear-time algorithm for solving the outer-paired domination problem on trees.

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41

Borowiecki, Mieczysław, and Ewa Drgas-Burchardt. "Acyclic homomorphisms to stars of graph Cartesian products and chordal bipartite graphs." Discrete Mathematics 312, no. 14 (July 2012): 2146–52. http://dx.doi.org/10.1016/j.disc.2011.08.030.

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42

Jiang, Huiqin, and Yongsheng Rao. "Total 2-Rainbow Domination in Graphs." Mathematics 10, no. 12 (June 14, 2022): 2059. http://dx.doi.org/10.3390/math10122059.

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A total k-rainbow dominating function on a graph G=(V,E) is a function f:V(G)→2{1,2,…,k} such that (i) ∪u∈N(v)f(u)={1,2,…,k} for every vertex v with f(v)=∅, (ii) ∪u∈N(v)f(u)≠∅ for f(v)≠∅. The weight of a total 2-rainbow dominating function is denoted by ω(f)=∑v∈V(G)|f(v)|. The total k-rainbow domination number of G is the minimum weight of a total k-rainbow dominating function of G. The minimum total 2-rainbow domination problem (MT2RDP) is to find the total 2-rainbow domination number of the input graph. In this paper, we study the total 2-rainbow domination number of graphs. We prove that the MT2RDP is NP-complete for planar bipartite graphs, chordal bipartite graphs, undirected path graphs and split graphs. Then, a linear-time algorithm is proposed for computing the total k-rainbow domination number of trees. Finally, we study the difference in complexity between MT2RDP and the minimum 2-rainbow domination problem.

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43

Chakradhar, P., and P. Venkata Subba Reddy. "Complexity issues of perfect secure domination in graphs." RAIRO - Theoretical Informatics and Applications 55 (2021): 11. http://dx.doi.org/10.1051/ita/2021012.

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Let G = (V, E) be a simple, undirected and connected graph. A dominating set S is called a secure dominating set if for each u ∈ V \ S, there exists v ∈ S such that (u, v) ∈ E and (S \{v}) ∪{u} is a dominating set of G. If further the vertex v ∈ S is unique, then S is called a perfect secure dominating set (PSDS). The perfect secure domination number γps(G) is the minimum cardinality of a perfect secure dominating set of G. Given a graph G and a positive integer k, the perfect secure domination (PSDOM) problem is to check whether G has a PSDS of size at most k. In this paper, we prove that PSDOM problem is NP-complete for split graphs, star convex bipartite graphs, comb convex bipartite graphs, planar graphs and dually chordal graphs. We propose a linear time algorithm to solve the PSDOM problem in caterpillar trees and also show that this problem is linear time solvable for bounded tree-width graphs and threshold graphs, a subclass of split graphs. Finally, we show that the domination and perfect secure domination problems are not equivalent in computational complexity aspects.

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44

Almulhim, Ahlam. "Total Perfect Roman Domination." Symmetry 15, no. 9 (August 31, 2023): 1676. http://dx.doi.org/10.3390/sym15091676.

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A total perfect Roman dominating function (TPRDF) on a graph G=(V,E) is a function f from V to {0,1,2} satisfying (i) every vertex v with f(v)=0 is a neighbor of exactly one vertex u with f(u)=2; in addition, (ii) the subgraph of G that is induced by the vertices with nonzero weight has no isolated vertex. The weight of a TPRDF f is ∑v∈Vf(v). The total perfect Roman domination number of G, denoted by γtRp(G), is the minimum weight of a TPRDF on G. In this paper, we initiated the study of total perfect Roman domination. We characterized graphs with the largest-possible γtRp(G). We proved that total perfect Roman domination is NP-complete for chordal graphs, bipartite graphs, and for planar bipartite graphs. Finally, we related γtRp(G) to perfect domination γp(G) by proving γtRp(G)≤3γp(G) for every graph G, and we characterized trees T of order n≥3 for which γtRp(T)=3γp(T). This notion can be utilized to develop a defensive strategy with some properties.

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45

Abbas, Nesrine, and Lorna Stewart. "Clustering bipartite and chordal graphs: Complexity, sequential and parallel algorithms." Discrete Applied Mathematics 91, no. 1-3 (January 1999): 1–23. http://dx.doi.org/10.1016/s0166-218x(98)00094-8.

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46

Abueida, Atif, Arthur H. Busch, and R. Sritharan. "A Min–Max Property of Chordal Bipartite Graphs with Applications." Graphs and Combinatorics 26, no. 3 (April 3, 2010): 301–13. http://dx.doi.org/10.1007/s00373-010-0922-0.

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47

Eto, Hiroshi, Fengrui Guo, and Eiji Miyano. "Distance- $$d$$ independent set problems for bipartite and chordal graphs." Journal of Combinatorial Optimization 27, no. 1 (January 10, 2013): 88–99. http://dx.doi.org/10.1007/s10878-012-9594-4.

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48

Llamas, Aurora, and Josá Martínez–Bernal. "Cover Product and Betti Polynomial of Graphs." Canadian Mathematical Bulletin 58, no. 2 (June 1, 2015): 320–33. http://dx.doi.org/10.4153/cmb-2015-013-3.

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AbstractThe cover product of disjoint graphs G and H with fixed vertex covers C(G) and C(H), is the graphwith vertex set V(G) ∪ V(H) and edge setWe describe the graded Betti numbers of GeH in terms of those of. As applications we obtain: (i) For any positive integer k there exists a connected bipartite graph G such that reg R/I(G) = μS(G) + k, where, I(G) denotes the edge ideal of G, reg R/I(G) is the Castelnuovo–Mumford regularity of R/I(G) and μS(G) is the induced or strong matching number of G; (ii)The graded Betti numbers of the complement of a tree depends only upon its number of vertices; (iii)The h-vector of R/I(G e H) is described in terms of the h-vectors of R/I(G) and R/I(H). Furthermore, in a diòerent direction, we give a recursive formula for the graded Betti numbers of chordal bipartite graphs.

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49

Chin-Wen, Ho, and Jou-Ming Chang. "Solving the all-pairs-shortest-length problem on chordal bipartite graphs." Information Processing Letters 69, no. 2 (January 1999): 87–93. http://dx.doi.org/10.1016/s0020-0190(98)00195-1.

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50

Panda, B. S., and D. Pradhan. "Locally connected spanning trees in cographs, complements of bipartite graphs and doubly chordal graphs." Information Processing Letters 110, no. 23 (November 2010): 1067–73. http://dx.doi.org/10.1016/j.ipl.2010.09.008.

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