Matchings in Random Biregular Bipartite Graphs
  We study the existence of perfect matchings in suitably chosen induced subgraphs of random biregular bipartite graphs. We prove a result similar to a classical theorem of Erdos and Renyi about perfect matchings in random bipartite graphs. We also present an application to commutative graphs, a class of graphs that are featured in additive number theory. 
Guillem Perarnau and Giorgis Petridis
math.CO