Perfect matchings in inhomogeneous random bipartite graphs in random environment

Abstract

In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erd\H os-R\'enyi random bipartite graphs in a random environment. We show that the expected number of perfect matchings obeys a precise asymptotic.

Keywords

• perfect matchings
• large permanents
• random graphs