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How is a Chordal Graph like a Supersolvable Binary Matroid? [PDF]
Discrete Mathematics, 2004 Let G be a finite simple graph. From the pioneering work of R. P. Stanley it is known that the cycle matroid of G is supersolvable iff G is chordal (rigid): this is another way to read Dirac's theorem on chordal graphs. Chordal binary matroids are not in
Cordovil, Raul +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.
Sunil Chandran +2 more
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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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Determining what sets of trees can be the clique trees of a chordal graph [PDF]
Journal of the Brazilian Computer Society, 2011 Chordal graphs have characteristic tree representations, the clique trees. The problems of finding one or enumerating them have already been solved in a satisfactory way. In this paper, the following related problem is studied: given a family T of trees,
de Caria, Pablo Jesús +1 more
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Branchwidth of chordal graphs [PDF]
Discrete Applied Mathematics, 2009 International ...
Christophe Paul, Jan Arne Telle
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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
openalex +7 more sources
Cohen-Macaulay chordal graphs [PDF]
arXiv, 2004 We classify all Cohen-Macaulay chordal graphs. In particular. it is shown that a chordal graph is Cohen-Macaulay if and only if its unmixed.
Juergen Herzog +2 more
arxiv +3 more sources
Discrete Mathematics, 1994 AbstractWe introduce the closed-neighborhood intersection multigraph as a useful multigraph version of the square of a graph. We characterize those multigraphs which are squares of chordal graphs and include an algorithm to go from the squared chordal graph back to its (unique!) square root. This becomes particularly simple in the case of k-trees, with
F. Harary, T. McKee
semanticscholar +2 more sources
The leafage of a chordal graph
Discussiones Mathematicae Graph Theory, 1998 The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes.
In-Jen Lin, T. McKee, D. West
semanticscholar +4 more sources
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
doaj +2 more sources