反超图的着色理论

The Theory of Upper Chromatic Number of Co-Hypergraphs

反超图及其上色数概念是由 Ｖｉｔａｌｙ Ｉ，Ｖｏｌｏｓｈｉｎ在文献［２］中提出来的．本文给出了点对图的概念，再将反超图的着色理论和图的连通性理论结合起来，给出了个正则反超图上色数为３的充要条件，并在此基础上得到了上色数为３的４－正则反起图的边数的一个下界．

The notion of upper chromatic number of a hypergraph was introduced by Vitaly I. Voloshin in [2]. In this paper,we introduce the notion of pair graph and give a necessary and sufficient condition for X (H) = 3,where H is a 4-uniform co-hypergraph,we also give a lower bond of e(H).