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823
On Some Cograph Extensions and Their Algorithms
, 1993
"... This paper reviews some classes of graphs related to cographs. The characterization of cographs by which there is no induced path on three edges (P 4 ) is relaxed in various ways. Considered are classes of graphs that are uniquely representable by trees. Three such classes studied here are: P 4 red ..."
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This paper reviews some classes of graphs related to cographs. The characterization of cographs by which there is no induced path on three edges (P 4 ) is relaxed in various ways. Considered are classes of graphs that are uniquely representable by trees. Three such classes studied here are: P 4
Partial and Perfect Path Covers of Cographs
, 1998
"... A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G. For fixed ..."
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Cited by 1 (0 self)
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A set P of disjoint paths in a graph G is called a (complete) path cover of G if every vertex of G belongs to one of the paths in P. A path cover of any subgraph of G is called a partial path cover of G. For fixed
On the bicoloring of cographs and . . .
"... A bcoloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The bchromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a bcoloring with t colors. A graph G ..."
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A bcoloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The bchromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a bcoloring with t colors. A graph G
Acyclic and Star Colorings of Cographs
, 2009
"... An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star coloring requires that the union of any two color classes induces a disjoint collection of stars. We prove that every acy ..."
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acyclic coloring of a cograph is also a star coloring and give a lineartime algorithm for finding an optimal acyclic and star coloring of a cograph. We also show that the acyclic chromatic number, the star chromatic number, the treewidth plus one, and the pathwidth plus one are all equal for cographs.
ON RETRACTS, ABSOLUTE RETRACTS, AND FOLDS IN COGRAPHS
"... Abstract. Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NPcomplete. We show that this problem is fixedparameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect g ..."
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Abstract. Let G and H be two cographs. We show that the problem to determine whether H is a retract of G is NPcomplete. We show that this problem is fixedparameter tractable when parameterized by the size of H. When restricted to the class of threshold graphs or to the class of trivially perfect
Contraction Degeneracy on Cographs
, 2004
"... The contraction degeneracy of a graph G is the maximum minimum degree of G # over all minors G # of G. The corresponding decision problem is known to be NPcomplete. In this ..."
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Cited by 4 (3 self)
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The contraction degeneracy of a graph G is the maximum minimum degree of G # over all minors G # of G. The corresponding decision problem is known to be NPcomplete. In this
Enumerative Aspects of Certain Subclasses of Perfect Graphs
"... We investigate the enumerative aspects of various classes of perfect graphs like cographs, split graphs, trivially perfect graphs and threshold graphs. For subclasses of permutation graphs like cographs and threshold graphs we also determine the number of permutations ß of f1; 2; : : : ; ng such tha ..."
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We investigate the enumerative aspects of various classes of perfect graphs like cographs, split graphs, trivially perfect graphs and threshold graphs. For subclasses of permutation graphs like cographs and threshold graphs we also determine the number of permutations ß of f1; 2; : : : ; ng
Results 1  10
of
823