具有最小连通点对图的C-超图的染色讨论

主要讨论C-超图的染色与点的点对图的连通性之间的关系,证明了对任意给定的不小于3的正整数n,都存在上色数为n且具有最小连通点对图的3一致C-超图.

On the coloring of C-hypergraphs with minimum connected pair graphs

The upper (lower) chromatic number X(H) of a mixed hypergraph H=(A,B,C) is the maximum (minimum) number of colors that can be assigned to the vertices of H in such a way that each C-edgecontains a monochromatic pair of vertices and each D-edge has two vertices colored differently. The upper (lower) chromatic number of a mixed hypergraph is colosely related to the number of edges, and the number of edges is colosely related to the connectness of the pair graphs of its vertices. In this paper we diascuss the relationship between the coloring and the connectess of the pair graphs of its vertices of a C-hypergraph, and we prove that for any positive integer n(≥3), there exists a 3-uniform C-hypergraph with upper chromatic number n and minimum connectedpair graphs.