Results 231 to 240 of about 2,481 (263)
Graph searching on chordal graphs
, 1996 Two variations of the graph searching problem, edge searching and node searching, are studied on several classes of chordal graphs, which include split graphs, interval graphs and k-starlike graphs.
Sheng-Lung Peng +4 more
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The dual polyhedron to the chordal graph polytope and the rebuttal of the chordal graph conjecture
International Journal of Approximate Reasoning, 2021 The integer linear programming approach to structural learning of decomposable graphical models led us earlier to the concept of a chordal graph polytope.
Milan Studený +2 more
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The clique-separator graph for chordal graphs
Discrete Applied Mathematics, 2009 We present a new representation of a chordal graph called the clique-separator graph, whose nodes are the maximal cliques and minimal vertex separators of the graph. We present structural properties of the clique-separator graph and additional properties
Louis Ibarra
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Journal of Graph Theory, 1993
AbstractThe chordality of a graph G = (V, E) is defined as the minimum k such that we can write E = E1 ∩ … ∩ Ek with each (V, Ei) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width.
Terry A. McKee, Edward R. Scheinerman
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AbstractThe chordality of a graph G = (V, E) is defined as the minimum k such that we can write E = E1 ∩ … ∩ Ek with each (V, Ei) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width.
Terry A. McKee, Edward R. Scheinerman
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SIAM Journal on Discrete Mathematics, 1994
The authors give a unified framework for characterizations of graphs which are dual (in the sense of hypergraphs) to chordal graphs, in terms of neighborhood and clique hypergraphs. By using the hypergraph approach in a systematical way, new results are obtained, a part of previous results are generalized, and some of the proofs are simplified.
Andreas Brandstädt +3 more
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The authors give a unified framework for characterizations of graphs which are dual (in the sense of hypergraphs) to chordal graphs, in terms of neighborhood and clique hypergraphs. By using the hypergraph approach in a systematical way, new results are obtained, a part of previous results are generalized, and some of the proofs are simplified.
Andreas Brandstädt +3 more
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Chordal Graph Models of Contingency Tables
Computers and Mathematics With Applications, 1997 Chordal graph theory has recently found application by statisticians in the analysis of contingency tables. Specifically, what are called \u27\u27decomposable loglinear models\u27\u27 correspond exactly to chordal graphs.
McKee, T.A. +3 more
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On the Hyperbolicity of Chordal Graphs
Annals of Combinatorics, 2001The hyperbolicity of a metric space is the infimum of all \(\delta\) for which \(d(x,y)+ d(u,v)\leq \max\{d(x, u)+ d(y,v), d(x,v)+ d(y,u)\}+ \delta\) for all elements \(x\), \(y\), \(u\), \(v\) from the space. The notion can be viewed as expressing how `tree like' the space is, as spaces with hyperbolicity \(0\) are precisely the metric trees.
Brinkmann, Gunnar +2 more
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Chromaticity of Chordal Graphs
Graphs and Combinatorics, 1997A chordal graph is a graph that does not contain any induced cycle with length greater than 3. A polynomial \(P=\lambda^{m_0}(\lambda-1)^{m_1}\cdots (\lambda-k)^{m_k}\) is said to be a chordal polynomial, if for any graph \(G\), \(P(G,\lambda)=P\) implies \(G\) is a chordal graph. The main result of this paper is the following: If \(m_0=1\) and \(\sum_{
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A generalization of chordal graphs
Journal of Graph Theory, 1984AbstractIn a 3‐connected planar triangulation, every circuit of length ≥ 4 divides the rest of the edges into two nontrivial parts (inside and outside) which are “separated” by the circuit. Neil Robertson asked to what extent triangulations are characterized by this property, and conjectured an answer.
Paul D. Seymour, R. W. Weaver
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Chordal graphs and their clique graphs
1995In the first part of this paper, a new structure for chordal graph is introduced, namely the clique graph. This structure is shown to be optimal with regard to the set of clique trees. The greedy aspect of the recognition algorithms of chordal graphs is studied.
Philippe Galinier +2 more
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