Towards random uniform sampling of bipartite graphs with given degree sequence

Abstract

In this paper we consider a simple Markov chain for bipartite graphs with given degree sequence on $n$ vertices. We show that the mixing time of this Markov chain is bounded above by a polynomial in $n$ in case of {\em semi-regular} degree sequence. The novelty of our approach lays in the construction of the canonical paths in Sinclair's method.Comment: 47 pages, submitted for publication. In this version we explain explicitly our main contribution and corrected a serious flaw in the cycle decompositio