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Journal articles on the topic 'Strongly chordal graphs'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Jeya Jothi, R. Mary, and A. Amutha. "Characterization of Super Strongly Perfect Graphs in Chordal and Strongly Chordal Graphs." Mapana - Journal of Sciences 11, no. 4 (2012): 121–31. http://dx.doi.org/10.12723/mjs.23.10.

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A Graph G is Super Strongly Perfect Graph if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal complete sub graphs of H. In this paper, we have investigated the characterization of Super Strongly Perfect graphs using odd cycles. We have given the characterization of Super Strongly Perfect graphs in chordal and strongly chordal graphs. We have presented the results of Chordal graphs in terms of domination and co - domination numbers γ and . We have given the relationship between diameter, domination and co - domination numbers of chordal graphs. Also w

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2

McKee, Terry A. "Strengthening strongly chordal graphs." Discrete Mathematics, Algorithms and Applications 08, no. 01 (2016): 1650002. http://dx.doi.org/10.1142/s1793830916500026.

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An [Formula: see text]-chord of a cycle [Formula: see text] is a chord that forms a new cycle with a length-[Formula: see text] subpath of [Formula: see text] when [Formula: see text] is at most half the length of [Formula: see text]. Define a graph to be [Formula: see text]-strongly chordal if, for every [Formula: see text], every cycle long enough to have an [Formula: see text]-chord always has an [Formula: see text]-chord. The [Formula: see text]-strongly chordal and [Formula: see text]-strongly chordal graphs are, respectively, the chordal and strongly chordal graphs. Several characterizat

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3

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

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4

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

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5

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

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6

McKee, Terry A. "Odd twists on strongly chordal graphs." Discrete Mathematics, Algorithms and Applications 11, no. 03 (2019): 1950034. http://dx.doi.org/10.1142/s1793830919500344.

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Strongly chordal graphs can be characterized as chordal graphs in which every even cycle of length at least [Formula: see text] has an odd chord (a chord whose endpoints are an odd distance apart in the cycle subgraph). Define “oddly chordal graphs” to be chordal graphs in which every odd cycle of length at least [Formula: see text] has an odd chord. Strongly chordal graphs are shown to be oddly chordal, and the oddly chordal graphs are characterized by forbidding induced “double [Formula: see text]-sun” subgraphs. Both strongly chordal and oddly chordal graphs are also characterized in terms

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7

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

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8

Guo, Jin, Yi-Huang Shen, and Tongsuo Wu. "Edgewise strongly shellable clutters." Journal of Algebra and Its Applications 17, no. 01 (2018): 1850018. http://dx.doi.org/10.1142/s0219498818500184.

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When [Formula: see text] is a chordal clutter in the sense of Woodroofe or Emtander, we show that the complement clutter is edgewise strongly shellable. When [Formula: see text] is indeed a finite simple graph, we provide additional characterization of chordal graphs from the point of view of strong shellability. In particular, the generic graph [Formula: see text] of a tree is shown to be bi-strongly shellable.

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9

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 (2010): 438–56. http://dx.doi.org/10.1007/s10878-010-9322-x.

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10

McKee, Terry A. "Symmetric graph-theoretic roles of two-pairs and chords of cycles." Discrete Mathematics, Algorithms and Applications 06, no. 03 (2014): 1450031. http://dx.doi.org/10.1142/s1793830914500311.

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Although the notion of a two-pair (a pair of vertices between which all induced paths have length 2) was invented for the class of weakly chordal graphs, two-pairs can also play a fundamental role for smaller graph classes. Indeed, two-pairs and chords of cycles can collaborate symmetrically to give parallel characterizations of weakly chordal, chordal, and strongly chordal graphs (and of distance-hereditary graphs).

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11

Dahlhaus, Elias, Paul D. Manuel, and Mirka Miller. "A characterization of strongly chordal graphs." Discrete Mathematics 187, no. 1-3 (1998): 269–71. http://dx.doi.org/10.1016/s0012-365x(97)00268-9.

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12

Liu, Chun-Hung, and Gerard J. Chang. "Roman domination on strongly chordal graphs." Journal of Combinatorial Optimization 26, no. 3 (2012): 608–19. http://dx.doi.org/10.1007/s10878-012-9482-y.

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13

Dahlhaus, Elias, and Marek Karpinski. "Matching and multidimensional matching in chordal and strongly chordal graphs." Discrete Applied Mathematics 84, no. 1-3 (1998): 79–91. http://dx.doi.org/10.1016/s0166-218x(98)00006-7.

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14

Panda, B. S., and Preeti Goel. "-labeling of dually chordal graphs and strongly orderable graphs." Information Processing Letters 112, no. 13 (2012): 552–56. http://dx.doi.org/10.1016/j.ipl.2012.04.003.

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15

McKee, Terry A. "A new characterization of strongly chordal graphs." Discrete Mathematics 205, no. 1-3 (1999): 245–47. http://dx.doi.org/10.1016/s0012-365x(99)00107-7.

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16

Rong, Guozhen, Wenjun Li, Jianxin Wang, and Yongjie Yang. "Cycle Extendability of Hamiltonian Strongly Chordal Graphs." SIAM Journal on Discrete Mathematics 35, no. 3 (2021): 2115–28. http://dx.doi.org/10.1137/20m1369920.

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17

Takaoka, Asahi. "Complexity of Hamiltonian Cycle Reconfiguration." Algorithms 11, no. 9 (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 pre

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18

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 (2007): 57–67. http://dx.doi.org/10.1016/j.tcs.2007.04.007.

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19

Dahlhaus, Elias, and Peter Damaschke. "The parallel solution of domination problems on chordal and strongly chordal graphs." Discrete Applied Mathematics 52, no. 3 (1994): 261–73. http://dx.doi.org/10.1016/0166-218x(94)90145-7.

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20

Campêlo, Manoel B., and Sulamita Klein. "Maximum vertex-weighted matching in strongly chordal graphs." Discrete Applied Mathematics 84, no. 1-3 (1998): 71–77. http://dx.doi.org/10.1016/s0166-218x(97)00136-4.

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21

White, Kevin, Martin Farber, and William Pulleyblank. "Steiner trees, connected domination and strongly chordal graphs." Networks 15, no. 1 (1985): 109–24. http://dx.doi.org/10.1002/net.3230150109.

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22

Brewster, Richard C., Gary MacGillivray, and Feiran Yang. "Broadcast domination and multipacking in strongly chordal graphs." Discrete Applied Mathematics 261 (May 2019): 108–18. http://dx.doi.org/10.1016/j.dam.2018.08.021.

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23

Balachandhran, V., and C. Pandu Rangan. "All-pairs-shortest-length on strongly chordal graphs." Discrete Applied Mathematics 69, no. 1-2 (1996): 169–82. http://dx.doi.org/10.1016/0166-218x(95)00088-9.

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24

Kaplan, Haim, Ron Shamir, and Robert E. Tarjan. "Tractability of Parameterized Completion Problems on Chordal, Strongly Chordal, and Proper Interval Graphs." SIAM Journal on Computing 28, no. 5 (1999): 1906–22. http://dx.doi.org/10.1137/s0097539796303044.

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25

De Caria, Pablo, and Terry A. McKee. "Maxclique and unit disk characterizations of strongly chordal graphs." Discussiones Mathematicae Graph Theory 34, no. 3 (2014): 593. http://dx.doi.org/10.7151/dmgt.1757.

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26

McKee, Terry A. "Strong clique trees, neighborhood trees, and strongly chordal graphs." Journal of Graph Theory 33, no. 3 (2000): 151–60. http://dx.doi.org/10.1002/(sici)1097-0118(200003)33:3<151::aid-jgt5>3.0.co;2-u.

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27

Chang, Gerard J., Bo-Jr Li, and Jiaojiao Wu. "Rainbow domination and related problems on strongly chordal graphs." Discrete Applied Mathematics 161, no. 10-11 (2013): 1395–401. http://dx.doi.org/10.1016/j.dam.2013.01.024.

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28

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 (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 chorda

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29

Kratsch, Dieter. "Finding dominating cliques efficiently, in strongly chordal graphs and undirected path graphs." Discrete Mathematics 86, no. 1-3 (1990): 225–38. http://dx.doi.org/10.1016/0012-365x(90)90363-m.

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30

Herzog, Jürgen, Satoshi Murai, Xinxian Zheng, Takayuki Hibi, and Ngô Viêt Trung. "Kruskal-Katona type theorems for clique complexes arising from chordal and strongly chordal graphs." Combinatorica 28, no. 3 (2008): 315–23. http://dx.doi.org/10.1007/s00493-008-2319-8.

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31

Lee, Chuan-Min. "Weighted Maximum-Clique Transversal Sets of Graphs." ISRN Discrete Mathematics 2011 (January 26, 2011): 1–20. http://dx.doi.org/10.5402/2011/540834.

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A maximum-clique transversal set of a graph G is a subset of vertices intersecting all maximum cliques of G. The maximum-clique transversal set problem is to find a maximum-clique transversal set of G of minimum cardinality. Motivated by the placement of transmitters for cellular telephones, Chang, Kloks, and Lee introduced the concept of maximum-clique transversal sets on graphs in 2001. In this paper, we study the weighted version of the maximum-clique transversal set problem for split graphs, balanced graphs, strongly chordal graph, Helly circular-arc graphs, comparability graphs, distance-

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32

Jose, Bibin K. "Some New Classes of Open Distance-Pattern Uniform Graphs." International Journal of Combinatorics 2013 (July 24, 2013): 1–7. http://dx.doi.org/10.1155/2013/863439.

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Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this pape

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33

Lin, Ching-Chi, Gerard J. Chang, and Gen-Huey Chen. "Locally connected spanning trees in strongly chordal graphs and proper circular-arc graphs." Discrete Mathematics 307, no. 2 (2007): 208–15. http://dx.doi.org/10.1016/j.disc.2006.06.026.

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34

Le, Van Bang, and Ngoc Tuy Nguyen. "A good characterization of squares of strongly chordal split graphs." Information Processing Letters 111, no. 3 (2011): 120–23. http://dx.doi.org/10.1016/j.ipl.2010.11.003.

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35

Chu, Kuan-Ting, Wu-Hsiung Lin, and Chiuyuan Chen. "Mutual transferability for (F,B,R)-domination on strongly chordal graphs and cactus graphs." Discrete Applied Mathematics 259 (April 2019): 41–52. http://dx.doi.org/10.1016/j.dam.2018.12.034.

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36

Dahlhaus, Elias. "A parallel algorithm for computing Steiner trees in strongly chordal graphs." Discrete Applied Mathematics 51, no. 1-2 (1994): 47–61. http://dx.doi.org/10.1016/0166-218x(94)90093-0.

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37

Nevries, Ragnar, and Christian Rosenke. "Characterizing and computing the structure of clique intersections in strongly chordal graphs." Discrete Applied Mathematics 181 (January 2015): 221–34. http://dx.doi.org/10.1016/j.dam.2014.09.003.

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38

Chen, Lei, Changhong Lu, and Zhenbing Zeng. "A linear-time algorithm for paired-domination problem in strongly chordal graphs." Information Processing Letters 110, no. 1 (2009): 20–23. http://dx.doi.org/10.1016/j.ipl.2009.09.014.

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39

Lin, Ching-Chi, Gerard J. Chang, and Gen-Huey Chen. "The degree-preserving spanning tree problem in strongly chordal and directed path graphs." Networks 56, no. 3 (2009): 183–87. http://dx.doi.org/10.1002/net.20359.

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40

Chang, Jou-Ming, Chiun-Chieh Hsu, Yue-Li Wang, and Ting-Yem Ho. "Finding the set of all hinge vertices for strongly chordal graphs in linear time." Information Sciences 99, no. 3-4 (1997): 173–82. http://dx.doi.org/10.1016/s0020-0255(96)00272-1.

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41

Peng, Shen-Lung, and Maw-Shang Chang. "A simple linear time algorithm for the domatic partition problem on strongly chordal graphs." Information Processing Letters 43, no. 6 (1992): 297–300. http://dx.doi.org/10.1016/0020-0190(92)90115-c.

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42

Dobson, M. P., V. Leoni, and G. Nasini. "The k-limited packing and k-tuple domination problems in strongly chordal, P4-tidy and split graphs." Electronic Notes in Discrete Mathematics 36 (August 2010): 559–66. http://dx.doi.org/10.1016/j.endm.2010.05.071.

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43

Lee, Hai-Yen, and Gerard J. Chang. "Thew-median of a connected strongly chordal graph." Journal of Graph Theory 18, no. 7 (1994): 673–80. http://dx.doi.org/10.1002/jgt.3190180704.

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44

Rahman, Md Zamilur, and Asish Mukhopadhyay. "Semi-dynamic algorithms for strongly chordal graphs." Discrete Mathematics, Algorithms and Applications, December 5, 2020, 2150049. http://dx.doi.org/10.1142/s179383092150049x.

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Within the broad ambit of algorithm design, the study of dynamic graph algorithms continues to be a thriving area of research. Commensurate with this interest is an extensive literature on the topic. Not surprisingly, dynamic algorithms for all varieties of shortest path problems, in view of their practical importance, occupy a preeminent position. Relevant to this paper are fully dynamic algorithms for chordal graphs. Surprisingly, to the best of our knowledge, there seems to be no reported results for the problem of dynamic algorithms for strongly chordal graphs. To redress this gap, in this

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45

Yetim, Mehmet Akif. "Coloring squares of graphs via vertex orderings." Discrete Mathematics, Algorithms and Applications, August 21, 2020, 2050093. http://dx.doi.org/10.1142/s1793830920500937.

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We provide upper bounds on the chromatic number of the square of graphs, which have vertex ordering characterizations. We prove that [Formula: see text] is [Formula: see text]-colorable when [Formula: see text] is a cocomparability graph, [Formula: see text]-colorable when [Formula: see text] is a strongly orderable graph and [Formula: see text]-colorable when [Formula: see text] is a dually chordal graph, where [Formula: see text] is the maximum degree and [Formula: see text] = max[Formula: see text] is the multiplicity of the graph [Formula: see text]. This improves the currently known upper

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46

Couto, Fernanda, Luerbio Faria та Sulamita Klein. "Chordal- (k,ℓ)and strongly chordal- (k,ℓ)graph sandwich problems". Journal of the Brazilian Computer Society 20, № 1 (2014). http://dx.doi.org/10.1186/s13173-014-0016-6.

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47

Martínez-Pérez, Álvaro. "Chordality Properties and Hyperbolicity on Graphs." Electronic Journal of Combinatorics 23, no. 3 (2016). http://dx.doi.org/10.37236/5315.

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Let $G$ be a graph with the usual shortest-path metric. A graph is $\delta$-hyperbolic if for every geodesic triangle $T$, any side of $T$ is contained in a $\delta$-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generalizations of being chordal. We find chordality properties that are weaker and stronger than being $\delta$-hyperbolic. Moreover, we obtain a characterization of being hyperbolic on terms

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