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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
Leizhen Cai, Derek G. Corneil
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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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ZOR Zeitschrift f�r Operations Research Methods and Models of Operations Research, 1990
Summary: The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods. In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.
Szczepan Perz, Stefan Rolewicz
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Summary: The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods. In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.
Szczepan Perz, Stefan Rolewicz
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Journal of Graph Theory, 2005 AbstractFor 1 ≤ d ≤ k, let Kk/d be the graph with vertices 0, 1, …, k − 1, in which i ∼j if d ≤ |i − j| ≤ k − d. The circular chromatic number χc(G) of a graph G is the minimum of those k/d for which G admits a homomorphism to Kk/d. The circular clique number ωc(G) of G is the maximum of those k/d for which Kk/d admits a homomorphism to G. A graph G is
Xuding Zhu
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Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Hougardy
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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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Information Processing Letters, 1983
Abstract A perfect stable in a graph G is a stable S with the property that any vertex of G is either in S or adjacent with at least two vertices which are in S. This concept is an obvious generalization of the notion of perfect matching. In this note, the problem of deciding if a given graph has a perfect stable is considered.
Cornelius Croitoru, Emilian Suditu
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Abstract A perfect stable in a graph G is a stable S with the property that any vertex of G is either in S or adjacent with at least two vertices which are in S. This concept is an obvious generalization of the notion of perfect matching. In this note, the problem of deciding if a given graph has a perfect stable is considered.
Cornelius Croitoru, Emilian Suditu
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Journal of Graph Theory, 1999
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Information Processing Letters, 1994
The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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The perfect graph approach to study the combinatorial structure of visibility graphs in polyominos can be traced back to a paper of Berge et al., who made a survey of results and a collection of problems related to polyominos. In more recent works, Rajeev, Motwani et al.
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Triangle-free strongly circular-perfect graphs
Discrete Mathematics, 2009 International audienceZhu introduced circular-perfect graphs as a superclass of the well-known perfect graphs and as an important χ-bound class of graphs with the smallest non-trivial χ-binding function χ(G)≤ω(G)+1.
Annegret K Wagler +2 more
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