منابع مشابه
On the Genus of a Random Graph
Let p = p(n) be a function of n with 0 < p < 1. We consider the random graph model G(n, p); that is, the probability space of simple graphs with vertex–set {1, 2, . . . , n} where two distinct vertices are adjacent with probability p and for distinct pairs these events are mutually independent. Archdeacon and Grable have shown that if p2(1−p2) ≥ 8(logn)/n, then the (orientable) genus of a rando...
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The purpose of this article is to introduce a new iterative algorithm with properties resembling real life bipartite graphs. The algorithm enables us to generate wide range of random bigraphs, which features are determined by a set of parameters. We adapt the advances of last decade in unipartite complex networks modeling to the bigraph setting. This data structure can be observed in several si...
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In 2001, two numerical experiments were performed to observe whether or not the second largest eigenvalue of the adjacency matrix for the random cubic bipartite graph approaches 2 √ 2 as the size of the graph increases. In the first experiment, by Kevin Chang, the graphs were chosen using an algorithm that constructed entirely new graphs at each step using three random permutations, in contrast...
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We investigate the genus g (n,m) of the Erdős-Rényi random graph G(n,m), providing a thorough description of how this relates to the function m = m(n), and finding that there is different behaviour depending on which ‘region’ m falls into. Existing results are known for when m is at most 2 +O(n2/3) and when m is at least ω ( n1+ 1 j ) for j ∈N, and so we focus on intermediate cases. In particul...
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Let G = Gn,n,p be the random bipartite graph on n+n vertices, where each e ∈ [n] appears as an edge independently with probability p. Suppose that each edge e is given an independent uniform exponential rate one cost. Let C(G) denote the expected length of the minimum cost perfect matching. We show that w.h.p. if d = np (log n) then E [C(G)] = (1 + o(1)) 2 6p . This generalises the well-known r...
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ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 2019
ISSN: 0008-414X,1496-4279
DOI: 10.4153/s0008414x19000440