Extensions to 2-Factors in Bipartite Graphs (original) (raw)

Abstract

A graph is $d$-bounded if its maximum degree is at most ddd. We apply the Ore-Ryser Theorem on fff-factors in bipartite graphs to obtain conditions for the extension of a 222-bounded subgraph to a 222-factor in a bipartite graph. As consequences, we prove that every matching in the 555-dimensional hypercube extends to a 222-factor, and we obtain conditions for this property in general regular bipartite graphs. For example, to show that every matching in a regular nnn-vertex bipartite graph extends to a 222-factor, it suffices to show that all matchings with fewer than n/3n/3n/3 edges extend to 222-factors.