English

Random Oxford Graphs

Probability 2007-05-23 v1

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 mm 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)(i,j) trees they contain. We compute the thresholds for the emergence of a giant component and for the graph to be connected.

Keywords

Cite

@article{arxiv.math/0406138,
  title  = {Random Oxford Graphs},
  author = {Jonah Blasiak and Rick Durrett},
  journal= {arXiv preprint arXiv:math/0406138},
  year   = {2007}
}