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Coloring Powers of Chordal Graphs
, 2003
"... We prove that the kth power G of a chordal graph G with maximum degree is O( )degenerated for even values of k and O( )degenerated for odd ones. In particular, this bounds the chromatic number (G ). The bound proven for odd values of k is the best possible. Another consequence ..."
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Cited by 18 (6 self)
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We prove that the kth power G of a chordal graph G with maximum degree is O( )degenerated for even values of k and O( )degenerated for odd ones. In particular, this bounds the chromatic number (G ). The bound proven for odd values of k is the best possible. Another consequence
On 2Subcolourings of Chordal Graphs
"... Abstract. A 2subcolouring of a graph is a partition of the vertices into two subsets, each inducing a P3free graph, i.e., a disjoint union of cliques. We give the first polynomial time algorithm to test whether a chordal graph has a 2subcolouring. This solves (for two colours) an open problem of ..."
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Abstract. A 2subcolouring of a graph is a partition of the vertices into two subsets, each inducing a P3free graph, i.e., a disjoint union of cliques. We give the first polynomial time algorithm to test whether a chordal graph has a 2subcolouring. This solves (for two colours) an open problem
Dually Chordal Graphs
 SIAM J. DISCRETE MATH
, 1998
"... Recently in several papers, graphs with maximum neighborhood orderings were characterized and turned out to be algorithmically useful. This paper gives a unified framework for characterizations of those graphs in terms of neighborhood and clique hypergraphs which have the Helly property and whose l ..."
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Cited by 33 (15 self)
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line graph is chordal. These graphs are dual (in the sense of hypergraphs) to chordal graphs. By using the hypergraph approach in a systematical way new results are obtained, some of the old results are generalized, and some of the proofs are simplified.
Geodeticity of the contour of chordal graphs
, 2005
"... A vertex v is a boundary vertex of a connected graph G if there exists a vertex u such that no neighbor of v is further away from u than v. Moreover, if no vertex in the whole graph V (G) is further away from u than v, then v is called an eccentric vertex of G. A vertex v belongs to the contour of G ..."
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Cited by 1 (1 self)
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of chordal graphs. Our main contributions are, firstly, obtaining a realization theorem involving the cardinalities of the periphery, the contour, the eccentric subgraph and the boundary, and secondly, proving both that the contour of every chordal graph is geodetic and that this statement is not true
Branchwidth of chordal graphs
, 2007
"... This paper revisits the ’branchwidth territories’ of Kloks, Kratochvíl and Müller [12] to provide a simpler proof and a faster algorithm for computing branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running time ..."
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This paper revisits the ’branchwidth territories’ of Kloks, Kratochvíl and Müller [12] to provide a simpler proof and a faster algorithm for computing branchwidth of an interval graph. We also generalize the algorithm to the class of chordal graphs, albeit at the expense of exponential running
EQUISTABLE CHORDAL GRAPHS
"... Abstract. A graph is called equistable when there is a nonnegative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a chordal graphs is equistable if and only if every two adjacent nonsimplicial vertices have a common ..."
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Abstract. A graph is called equistable when there is a nonnegative weight function on its vertices such that a set S of vertices has total weight 1 if and only if S is maximal stable. We show that a chordal graphs is equistable if and only if every two adjacent nonsimplicial vertices have a
Chordal Graphs: Their Testing and Their Role
, 1994
"... This report is twofold. We first briefly discuss the role of chordal graphs for Gaussian elimination in sparse matrices and their role in the area of probabilistic reasoning in expert systems. In the second part we address the problem of testing whether a graph is chordal or not. If it is not, we pr ..."
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Cited by 2 (1 self)
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This report is twofold. We first briefly discuss the role of chordal graphs for Gaussian elimination in sparse matrices and their role in the area of probabilistic reasoning in expert systems. In the second part we address the problem of testing whether a graph is chordal or not. If it is not, we
Precoloring extension on chordal graphs
 In Graph Theory in Paris. Proceedings of a Conference in Memory of Claude Berge, Trends in Mathematics
, 2004
"... In the precoloring extension problem (PrExt) we are given a graph with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper kcoloring of the graph. 1PrExt is the special case where every color is assigned to at most one vertex i ..."
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Cited by 11 (3 self)
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in the precoloring. Answering an open question of Hujter and Tuza [HT96], we show that the 1PrExt problem can be solved in polynomial time for chordal graphs. 1
Graph Searching on Chordal Graphs
, 1997
"... In the graph searching problem, initially a graph with all edges contaminated is presented. We would like to obtain a state of the graph in which all edges are simultaneously clear by a sequence of moves using searchers. The objective is to achieve the desired state by using the least number of sear ..."
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Cited by 4 (1 self)
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of its endpoints. In this paper, we present a uniform approach to solve the above two graph searching problems on several classes of chordal graphs. For edge searching problem, we give an O(mn 2 )time algorithm on split graphs, an O(m + n)time algorithm on interval graphs, and an O(mn k )time
On bperfect chordal graphs
, 2007
"... The bchromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the bchromatic number is eq ..."
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Cited by 4 (1 self)
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The bchromatic number of a graph G is the largest integer k such that G has a coloring of the vertices in k color classes such that every color class contains a vertex that has a neighbour in all other color classes. We characterize the class of chordal graphs for which the bchromatic number
Results 11  20
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4,442