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Graphs and Combinatorics, 1991
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On hypergraph acyclicity and graph chordality
Information Processing Letters, 1988Concepts of acyclicity in hypergraphs and chordality in graphs are related by showing that a hierarchy of well-studied classes of chordal graphs corresponds to the hierarchy of classes of acyclic hypergraphs studied in relational database theory [\textit{R. Fagin}, J. Assoc. Comput. Mach. 30, 514-550 (1983; Zbl 0624.68088)].
D'ATRI, Alessandro, MOSCARINI, Marina
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Clique Partitions of Chordal Graphs
Combinatorics, Probability and Computing, 1993To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.
Paul Erdös +2 more
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What Is between Chordal and Weakly Chordal Graphs?
2008An (h ,s ,t )-representation of a graph G consists of a collection of subtrees {S v | v *** V (G )} of a tree T , such that (i) the maximum degree of T is at most h , (ii) every subtree has maximum degree at most s , and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in ...
Elad Cohen +3 more
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Dominating Sets in Chordal Graphs
SIAM Journal on Computing, 1982A set of vertices D is a dominating set for a graph if every vertex is either in D or adjacent to a vertex which is in D. We show that the problem of finding a minimum dominating set in a chordal graph is NP-complete, even when restricted to undirected path graphs, but exhibit a linear time greedy algorithm for the problem further restricted to ...
Kellogg S. Booth, J. Howard Johnson
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Chordal graphs, interval graphs, and wqo
Journal of Graph Theory, 1998Let \(\preceq\) be the induced-minor relation. It is shown that, for every \(t\), all chordal graphs of clique number at most \(t\) are well-quasi-ordered by \(\preceq\). On the other hand, if the bound on the clique number is dropped, even the class of interval graphs is not well-quasi-ordered by \(\preceq\).
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Intersection graphs of induced subtrees of any graph and a generalization of chordal graphs
Discrete Applied Mathematics, 2022Pablo de CARIA, Pablo de CARIA
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Reconfiguration graph for vertex colourings of weakly chordal graphs
Discrete Mathematics, 2020Carl Feghali, Jir̂Í Fiala
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On groups with chordal power graph, including a classification in the case of finite simple groups
Journal of Algebraic Combinatorics, 2023Eda Kaja
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