强二部超图的饱和数

Saturation number of strong bipartite hypergraphs

给定r-图F,称一个r-图G是F-饱和的,如果G不包含F,但是对于每条满足e∈E(G)的r-边e,G添加该边后会包含F,其中G表示G的补图.r-图F的饱和数,记为sat_(r)(n,F),指的是n个顶点的F-饱和r-图的最小边数.令S_(l)^(r),m为一个有l+m个顶点的r-图,其边集合由所有与某固定?-集合交集非空的边组成.一个关于sat_(r)(n,S_(l)^(r),m)渐进值的猜想于2004年被提出.给出了sat;(n,S_(l)^(r),m)的界.

Given an r-graph F,an r-graph G is F-saturated if G is F-free but adding any new edge e to G creates a copy of F for every r-edge e∈E(G)where G denotes the complement of G.For an r-graph F,the saturation function satr(n,F)is the minimum number of edges that an F-saturated graph on n vertices can have.Let S_(l)^(r),m have l+m vertices and consist of all edges intersecting some fixed l-set of vertices.A conjecture on the asymptotic value of sat;(n,S_(l)^(r),m)was proposed in 2004.In this paper,we prove bounds for sat;(n,S_(l)^(r),m).