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568
Chordal Graphs and Their Clique Graphs
 IN WG ’95
, 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. A new greedy algorithm that generali ..."
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Cited by 20 (7 self)
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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. A new greedy algorithm
Chordal Graphs and Their Clique Graphs
, 2014
"... In this paper, we present a new structure for chordal graph. We have also given the algorithm for MCS (Maximal Cardinality Search) and lexicographic BFS (Breadth First Search) which is used in two linear time and space algorithm. Also we discuss how to build a clique tree of a chordal graph and the ..."
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In this paper, we present a new structure for chordal graph. We have also given the algorithm for MCS (Maximal Cardinality Search) and lexicographic BFS (Breadth First Search) which is used in two linear time and space algorithm. Also we discuss how to build a clique tree of a chordal graph
Generalized Strongly Chordal Graphs
, 1993
"... This paper discusses a generalization of strongly chordal graphs. We consider characteristic elimination orderings for these graphs and prove the perfectness of these graphs. ..."
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Cited by 2 (0 self)
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This paper discusses a generalization of strongly chordal graphs. We consider characteristic elimination orderings for these graphs and prove the perfectness of these graphs.
On the Hyperbolicity of Chordal Graphs
 ANNALS OF COMBINATORICS
, 2001
"... The hyperbolicity δ 0 of a metric space in Gromov's sense can be viewed as a measure of how treelike the space is, since those spaces for which δ = 0 holds are precisely the set of (metric) trees. Here, we show that any chordal graph equipped with the usual graph metric is in this sense ..."
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Cited by 12 (0 self)
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The hyperbolicity δ 0 of a metric space in Gromov's sense can be viewed as a measure of how treelike the space is, since those spaces for which δ = 0 holds are precisely the set of (metric) trees. Here, we show that any chordal graph equipped with the usual graph metric
Cuts and Connectivity in Chordal Graphs
"... A cut (A; B) in a graph G is called internal, i N(A) 6= B and N(B) 6= A. In this paper, we study the structure of internal cuts in chordal graphs. We show that if (A; B) is an internal cut in a chordal graph, then for each i, 0 i (G)+1, there exists a clique K i such that jK i j = (G)+1, jK i ..."
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A cut (A; B) in a graph G is called internal, i N(A) 6= B and N(B) 6= A. In this paper, we study the structure of internal cuts in chordal graphs. We show that if (A; B) is an internal cut in a chordal graph, then for each i, 0 i (G)+1, there exists a clique K i such that jK i j = (G)+1, jK i
On Powers of Chordal Graphs And Their Colorings
 Congr. Numer
, 2000
"... The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs of t ..."
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Cited by 24 (1 self)
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The kth power of a graph G is a graph on the same vertex set as G, where a pair of vertices is connected by an edge if they are of distance at most k in G. We study the structure of powers of chordal graphs and the complexity of coloring them. We start by giving new and constructive proofs
THE LEAFAGE OF A CHORDAL GRAPH
, 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. The maximum of l(G) on nvertex graphs is n − lg n − 1 2 lg lg n + O(1). The proper ..."
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Cited by 2 (0 self)
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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. The maximum of l(G) on nvertex graphs is n − lg n − 1 2 lg lg n + O(1). The proper
Strictly chordal graphs and . . .
, 2005
"... A phylogeny is the evolutionary history for a set of evolutionarily related species. The development of hereditary trees, or phylogenetic trees, is an important research subject in computational biology. One development approach, motivated by graph theory, constructs a relationship graph based on ev ..."
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. In this thesis, we give a polynomial time algorithm to solve this problem for strictly chordal graphs, a particular subclass of chordal graphs. During the construction of a solution, we examine the problem for tree chordal graphs, and establish new properties for strictly chordal graphs.
Centers of Chordal Graphs
 GRAPHS AND COMBINATORICS
, 1991
"... In a graph G = (V, E), the eccentricity e(S) of a subset S _ ~ V is max ~ v mint ~ s d(x, y); and e(x) stands for e({x}). The diameter of G is maxx ~ v e(x), the radius r(G) of G is mine v e(x) and the clique radius cr(G) is mine(K) where K runs over all cliques. The center of G is the subgraph indu ..."
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Cited by 4 (0 self)
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induced by C(G), the set of all vertices x with e(x) = r(G). A clique center is a clique K with e(K) = cr(G). In this paper, we study the problem of determining the centers of chordal graphs. It is shown that the center of a connected chordal graph is distance invariant, biconnected and of diameter
Chordal graphs and the characteristic polynomial
"... Abstract A characteristic polynomial was recently deÿned for greedoids, generalizing the notion for matroids. When chordal graphs are viewed as antimatroids by shelling of simplicial vertices, the greedoid characteristic polynomial gives additional information about those graphs. In particular, the ..."
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Cited by 1 (0 self)
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Abstract A characteristic polynomial was recently deÿned for greedoids, generalizing the notion for matroids. When chordal graphs are viewed as antimatroids by shelling of simplicial vertices, the greedoid characteristic polynomial gives additional information about those graphs. In particular
Results 1  10
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568