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2011•Journal of Xinjiang Normal UniversityRequires access

An Extension of The Perfect Graph in Hypergraphs

Lin Sun

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Abstract

In the context of the perfect graphs,it is known that a graph G is perfect if G and each of its induced subgraphs have the property that the chromatic number x equals the size of a maximum clique ω.In this paper we define the weak k-perfect hypergraph and the strong k-perfect one,the definition makes the family of the perfect graphs be a special case.Furthermore,we discuss the properties of the k-perfect hypergraph and the strong k-perfect one,and obtain a theorem that can not be got directly from the corresponding theorem of Lovasz's.

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What this paper is about

In the context of the perfect graphs,it is known that a graph G is perfect if G and each of its induced subgraphs have the property that the chromatic number x equals the size of a maximum clique ω.In this paper we define the weak k-perfect hypergraph and the strong k-perfect one,the definition makes the family of the perfect graphs be a special case.Furthermore,we discuss the properties of the k-perfect hypergraph and the strong k-perfect one,and obtain a theorem that can not be got directly from the corresponding theorem of Lovasz's.

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Available abstract

In the context of the perfect graphs,it is known that a graph G is perfect if G and each of its induced subgraphs have the property that the chromatic number x equals the size of a maximum clique ω.In this paper we define the weak k-perfect hypergraph and the strong k-perfect one,the definition makes the family of the perfect graphs be a special case.Furthermore,we discuss the properties of the k-perfect hypergraph and the strong k-perfect one,and obtain a theorem that can not be got directly from the corresponding theorem of Lovasz's.

Key concepts: Perfect graph theorem, Trivially perfect graph, Perfect graph, Mathematics, Hypergraph, Combinatorics, Strong perfect graph theorem, Perfect power

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