Results 231 to 240 of about 12,385 (266)

On the chordality of a graph

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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Chromaticity of Chordal Graphs

Graphs and Combinatorics, 1997
A 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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On the Hyperbolicity of Chordal Graphs

Annals of Combinatorics, 2001
The 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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A generalization of chordal graphs

Journal of Graph Theory, 1984
AbstractIn 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

1995
In 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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