r-一致D-超图的最大边数

The Maximum Number of Hyperedges of An r-Uniform D-Hypergraph

混合超图H=(X,C,D)是一个三元组,其中X为H的顶点集。C为X的子集族,记作C-边。D为X的子集族,记作D-边。C=?的混合超图称为D-超图,D=?的混合超图称为C-超图。H=(X,C,D)是一混合超图,r是不小于2的正整数,若满足对任意的C-超边和D-超边,都有|C|=r,|D|=r,则称混合超图H为r-一致混合超图。特别地,若又有C=?,则称混合超图H为r-一致D超图。在本文中,我们解决当χ(H)=k时,r-一致D-超图H的最大边数这一问题。

A mixed hypergraph on a finite set X is a triple H=(X,C,D), where C and D are families of subset of X. The member of C is called C-edge and the member of D is called D-edge. A mixed hypergraph is called C-hypergraph when D=?, a mixed hypergraph is called D-hypergraph when C=?. Let H=(X,C,D) be a mixed hypergraph, r is a positive integer not less than 2. For an arbitrary C-edge and D-edge, if we have |C|=r,|D|=r, then the mixed hypergraph H is called r-uniform mixed hypergraph. In particular, if , the mixed hypergraph H is called r-uniform mixed D-hypergraph. In this paper, we solve the problem about the maximum number of hyperedges of an r-uniform D-hypergraph when χ(H)=k.