完美图在超图上的推广  

An Extension of The Perfect Graph in Hypergraphs

作　　者：孙林[1] 

机构地区：[1]昌吉学院数学系,新疆昌吉831100

出　　处：《新疆师范大学学报（自然科学版）》2011年第1期88-90,共3页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：昌吉学院研究生科研启动基金项目(09SSQD027)

摘　　要：由完美图知道,如果图G和它的每一个诱导子图均满足其色数x等于其最大团的基数ω,则图G是完美的。在这篇论文中,定义了弱k-完美超图和强k-完美超图。在这个定义之下,完美图是超图的一个特殊情况。进一步,讨论了弱k-完美超图和强k-完美超图的性质,并且得出了一个定理,该定理不能由Lovasz的相应定理直接推广而来。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.

关 键 词：弱k-完美超图 强k-完美超图 k-团 

分 类 号：O157.5[理学—数学]