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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
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.
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 ot ..."
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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
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
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.
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 1 (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
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 (5 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
Graph Colorings on Chordal Graphs
"... Since chordal graphs possess an excellent ("perfect") property on ordinary (vertex) coloring, it is interesting to see what would happen on different colorings. In this talk, we define two graph colorings (or labellings) on a simple graph G = (V; E). First, given positive integers m,n, an ..."
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Since chordal graphs possess an excellent ("perfect") property on ordinary (vertex) coloring, it is interesting to see what would happen on different colorings. In this talk, we define two graph colorings (or labellings) on a simple graph G = (V; E). First, given positive integers m
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.
Results 1  10
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5,538