Random Subgraphs in Cartesian Powers of Regular Graphs

  • Felix Joos

Abstract

Let G be a connected d-regular graph with k vertices. We investigate the behaviour of a spanning random subgraph Gnp of Gn, the n-th Cartesian power of G, which is constructed by deleting each edge independently with probability 1p. We prove that lim, if p=p(n)=1-\left(\frac{\lambda_n^{1/n}}{k}\right)^{1/d} and \lambda_n \rightarrow \lambda>0 as n \rightarrow \infty. This extends a result of L. Clark, Random subgraphs of certain graph powers, Int. J. Math. Math. Sci., 32(5):285-292, 2002.

Published
2012-02-23
Article Number
P47