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.
The upper (lower) chromatic number X^-, (H) of a mixed hypergraph H= (X, L .D ) 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 closely related to the number of edges, and the number of edges is closely related to the connectness of the pair graphs of its vertices. The relationship between the coloring and the connectness of the pair graphs of its vertices of a C-hypergraph is discussed, and it is proved that for any positive integer n(w≥3), there exists a 3-uniform C-hypergraph with upper chromatic number n and minimum connectedpair graphs.