Results 271 to 280 of about 38,756 (312)
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Cybernetics, 1990
The idea of an \(\omega\)-perfect graph is introduced. Several classes of \(\omega\)-perfect graphs are described, but the question of describing the whole class of \(\omega\)-perfect graphs is not clear yet. A vertex colouring algorithm is suggested for graphs which contain an odd number of holes, where the number of colours used does not exceed the ...
S. E. Markosyan, G. S. Gasparyan
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The idea of an \(\omega\)-perfect graph is introduced. Several classes of \(\omega\)-perfect graphs are described, but the question of describing the whole class of \(\omega\)-perfect graphs is not clear yet. A vertex colouring algorithm is suggested for graphs which contain an odd number of holes, where the number of colours used does not exceed the ...
S. E. Markosyan, G. S. Gasparyan
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A generalization of perfect graphs?i-perfect graphs
Journal of Graph Theory, 1996The \(i\)-chromatic number of \(G\), denoted \(\chi_i(G)\), is the least number \(k\) such that there is a \(k\)-colouring with no colour class inducing a \(K_{i+1}\) as a subgraph. The \(i\)-clique number, \(\omega_i(G)\), is defined to be \(\lceil \omega(G)/i\rceil\). An induced subgraph \(H\) of \(G\) is an \(i\)-transversal iff \(\omega(H)= i\) and
Cai, Leizhen, Corneil, Derek
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Combinatorica, 1992
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KORNER, JANOS +2 more
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KORNER, JANOS +2 more
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Perfect Graphs, Partitionable Graphs and Cutsets
Combinatorica, 2002We prove a theorem about cutsets in partitionable graphs that generalizes earlier results on amalgams, 2-amalgams and homogeneous pairs.
CONFORTI, MICHELANGELO +3 more
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Cycle‐perfect graphs are perfect
Journal of Graph Theory, 1996Given any graph \(G\), the cycle graph \(C(G)\) of \(G\) is defined by letting the vertices of \(C(G)\) be the induced cycles of \(G\); two induced cycles of \(G\) are adjacent in \(C(G)\) if they have in \(G\) at least one edge in common. \(G\) is called cycle-perfect if \(G\) and \(C(G)\) have no chordless cycles of odd length at least five.
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Neighbourhood-Perfect Line Graphs
Graphs and Combinatorics, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rank-perfect and" weakly rank-perfect graphs
Mathematical Methods of Operations Research (ZOR), 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2015
In this paper, we generalize the concept of {\it{perfect graphs}} to other parameters related to graph vertex coloring. This idea was introduced by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let $ a,b \in \{ , , , , \} $ where $ $ is the clique number, $ $ is the chromatic number, $ $ is the Grundy number, $ $ is the ...
Araujo-Pardo, G., Rubio-Montiel, C.
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In this paper, we generalize the concept of {\it{perfect graphs}} to other parameters related to graph vertex coloring. This idea was introduced by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let $ a,b \in \{ , , , , \} $ where $ $ is the clique number, $ $ is the chromatic number, $ $ is the Grundy number, $ $ is the ...
Araujo-Pardo, G., Rubio-Montiel, C.
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Graphs and Combinatorics, 1991
Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986.
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Proved are three theorems presenting upper and lower bounds of the minimum number of perfect subgraphs covering or partitioning either the vertex set or the edge set of a given graph. The weighted versions of both cases are studied, too. All the theorems are based on four lemmas, one of which being proved and published by the author in 1986.
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1984
In this paper, we investigate the class of graphs containing a set of vertices which meets exactly once every maximal clique.
C. Berge, P. Duchet
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In this paper, we investigate the class of graphs containing a set of vertices which meets exactly once every maximal clique.
C. Berge, P. Duchet
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