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The Neighborhood Polynomial of Chordal Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor.
Helena Bergold +2 more
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Graphs of low chordality [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 The chordality of a graph with at least one cycle is the length of the longest induced cycle in it. The odd (even) chordality is defined to be the length of the longest induced odd (even) cycle in it. Chordal graphs have chordality at most 3. We show that co-circular-arc graphs and co-circle graphs have even chordality at most 4.
Sunil L Chandran +2 more
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Treewidth of Chordal Bipartite Graphs [PDF]
Journal of Algorithms, 1995 Chordal bipartite graphs are exactly those bipartite graphs in which every cycle of length at least six has a chord. The treewidth of a graph G is the smallest maximum cliquesize among all chordal supergraphs of G decreased by one. We present a polynomial time algorithm for the exact computation of the treewidth of all chordal bipartite graphs.
Ton Kloks, Dieter Kratsch
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Branchwidth of chordal graphs [PDF]
Discrete Applied Mathematics, 2009 This paper revisits the ‘branchwidth territories' of Kloks, Kratochvíl and Müller [T. Kloks, J. Kratochvíl, H. Müller, New branchwidth territories, in: 16th Ann. Symp. on Theoretical Aspect of Computer Science, STACS, in: Lecture Notes in Computer Science, vol. 1563, 1999, pp.
Christophe Paul, Jan Arne Telle
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An Edge-Signed Generalization of Chordal Graphs, Free Multiplicities on Braid Arrangements, and Their Characterizations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 In this article, we propose a generalization of the notion of chordal graphs to signed graphs, which is based on the existence of a perfect elimination ordering for a chordal graph. We give a special kind of filtrations of the generalized chordal graphs,
Takuro Abe, Koji Nuida, Yasuhide Numata
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Discrete Applied Mathematics, 2008 AbstractPolar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NP-complete to decide for general graphs. It has been recently proved that for cographs, the existence of such a partition can be characterized by finitely many forbidden subgraphs,
Tınaz Ekim +3 more
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Chordal multipartite graphs and chordal colorings
Discrete Mathematics, 2007 Abstract‘Chordal multipartite graphs’ are properly colored graphs such that two vertices in a minimal vertex separator are adjacent if and only if they are differently colored. They have induced cycle characterizations that transcend those of chordal and chordal bipartite graphs.
Terry A. McKee
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On the complexity of the sandwich problems for strongly chordal graphs and chordal bipartite graphs
Theoretical Computer Science, 2007 AbstractGolumbic, Kaplan, and Shamir, in their paper [M.C. Golumbic, H. Kaplan, R. Shamir, Graph sandwich problems, J. Algorithms 19 (1995) 449–473] on graph sandwich problems published in 1995, left the status of sandwich problems for strongly chordal graphs and chordal bipartite graphs open.
Celina M.H. de Figueiredo +3 more
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On chordal phylogeny graphs [PDF]
Discrete Applied Mathematics, 2021 An acyclic digraph each vertex of which has indegree at most $i$ and outdegree at most $j$ is called an $(i, j)$ digraph for some positive integers $i$ and $j$. Lee {\it et al.} (2017) studied the phylogeny graphs of $(2, 2)$ digraphs and gave sufficient conditions and necessary conditions for $(2, 2)$ digraphs having chordal phylogeny graphs.
Soogang Eoh, Suh-Ryung Kim
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Properties and Recognition of Atom Graphs
Algorithms, 2022 The atom graph of a connected graph is a graph whose vertices are the atoms obtained by clique minimal separator decomposition of this graph, and whose edges are the edges of all its atom trees.
Geneviève Simonet, Anne Berry
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