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In this paper the authors generalize the classic random bipartite graph model, and define a model of the random bipartite multigraphs as follows:let m = m(n) be a positive integer-valued function on n and ζ(n,m;{pk}) the probability space consisting of all the labeled bipartite multigraphs with two vertex sets A ={a1,a2,...,an} and B = {b1,b2,...,bm}, in which the numbers tai,bj of the edges between any two vertices ai∈A and bj∈ B are identically distributed independent random variables with distribution P{tai,bj=k}=pk,k=0,1,2,...,where pk ≥0 and ∞Σk=0 pk=1. They obtain that Xc,d,A, the number of vertices in A with degree between c and d of Gn,m∈ζ(n, m;{pk}) has asymptotically Poisson distribution, and answer the following two questions about the space ζ(n,m;{pk}) with {pk} having geometric distribution, binomial distribution and Poisson distribution, respectively. Under which condition for {pk} can there be a function D(n) such that almost every random multigraph Gn,m∈ζ(n,m;{pk}) has maximum degree D(n)in A? under which condition for {pk} has almost every multigraph G(n,m)∈ζ(n,m;{pk}) a unique vertex of maximum degree in A? 相似文献
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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. 相似文献
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假设c是一个小于1/1152的常数,证明:对于每个充分大的偶数n,如果一个具有n个顶点的3一致完全超图的边着色满足每种颜色出现的次数不超过[cn],那么必含有一个每条边颜色都不一样的彩色哈密顿圈。 相似文献
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