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Random Oxford Graphs

Jonah Blasiak·Rick Durrett
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Abstract

Inspired by a concept in comparative genomics, we investigate properties of randomly chosen members of G_1(m,n,t), the set of bipartite graphs with $m$ left vertices, n right vertices, t edges, and each vertex of degree at least one. We give asymptotic results for the number of such graphs and the number of $(i,j)$ trees they contain. We compute the thresholds for the emergence of a giant component and for the graph to be connected.

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Jonah Blasiak, Rick Durrett. 2004-06-08. Random Oxford Graphs. https://arxiv.org/abs/math/0406138

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