Author:
BALISTER PAUL,BOLLOBÁS BÉLA
Abstract
Given a locally finite connected infinite graphG, let the interval [pmin(G),pmax(G)] be the smallest interval such that ifp>pmax(G), then every 1-independent bond percolation model onGwith bond probabilityppercolates, and forp<pmin(G) none does. We determine this interval for trees in terms of the branching number of the tree. We also give some general bounds for other graphsG, in particular for lattices.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,Computational Theory and Mathematics,Statistics and Probability,Theoretical Computer Science
Cited by
2 articles.
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