r-一致D-超图的最大边数
The Maximum Number of Hyperedges of An r-Uniform D-Hypergraph
摘要:
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。
Abstract:
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.
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