Let H be a fixed r-uniform hypergraph on h vertices and H a r-uniform hypergraph on n vertices. An H-factor of H is a spanning subhypergraph of H consisting of n/h vertex disjoint copies of H. The fractional arboricity of H is α(H) = max{|E'|/|V'|-1}, where the maximum is taken over all subhypergraphs (V', E') of H with |V'| > 1. Let δ(H) denote the minimum degree of vertices of H, where the degree of a vertex is the number of edges adjacent to it. In this paper we show that if δ(H) < α(H) then p = p(n) =n-1/α(H) is a sharp threshold function for the property that the random r-uniform hypergraph Hr(n,p) contains an H-factor, i. e. there are two positive constants c and C so that for p = p(n) = cn-1/α(H), almost surely Hr(n,p) does not contain an H-factor, whereas for p = p(n) =Cn-1/α(H), almost surely Hr(n,p) contains an H-factor (provided h divides n).%假设H和H分别是具有h个顶点和n个顶点的r一致超图.我们称一个具有n/h个分支,且每个分支都同构于H的H的生成子图为H的一个H-因子.记α(H)=max{|E'|/|V'|-1},其中的最大值取遍H的所有满足|V'|>1的子超图(V',E').δ(H)表示超图H的最小度.在本文中,我们证明了如果δ(H)<α(H),那么P=p(n)=n-1/α(H)就是随机超图Hr(n,p)包含H-因子的一个紧的门槛函数.也就是说,存在两个常数c和C使得对任意P=p(n)=cn-1/α(H),几乎所有的随机超图Hr(n,p)都不包含一个H-因子,对任意P=p(n)=Cn-1/α(H),几乎所有的随机超图Hr(n,P)都包含一个H-因子.
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