一类超图的异色数

摘要

At-coloring of a hypergraph H=(V,E) is a surjective mapping from the vertex set V onto a t-element set.A t-coloring f of H separates an edge α∈E if the images of the vertices in α under f are all different.We call f heterochromatic if f separates at least one edge of H,otherwise f,noheterochromatic.The heterochromatic number of H, denoted by hc(H),is the minimum positive integer t for which any t-coloring of H is heterochromatic.In this paper,we introduce a class of hypergraphs and obtain their heterochromatic numbers.%一个超图H=(V,E)的一个t着色是从V到一个t元集的满射,称H的一个t着色f分离H的一条边α∈E(G)如果|f(α)|=|α|.称f为异色的如果f分离H的至少一条边,否则f为非异色.H的异色数,记为hc(H),是最小的数t使得任一个着色都是异色的.在本文中,我们引进一类超图,并确定了它们的异色数.