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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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Clique Partitions of Chordal Graphs

Combinatorics, Probability and Computing, 1993
To 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.
Erdős, Paul   +2 more
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Dominating Sets in Chordal Graphs

SIAM Journal on Computing, 1982
A 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 ...
Booth, Kellogg S., Johnson, J. Howard
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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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Matrix Completions and Chordal Graphs

Acta Mathematica Sinica, English Series, 2003
This paper is an introduction to few problems and results in matrix completion problems. The topics which are considered here include questions on norm completions, rank completions, positive definite completions, numerical range completion properties and rank decomposability.
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