It is well known that every bipartite graph with vertex classes of size n whose minimum degree is at least n/2 contains a perfect matching. We prove an analogue of this result for...
The forcing number of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matching of G. In this paper, we demon...
Abstract. In this paper, we address the problem of computing a maximum-size subgraph of a P4-sparse graph which admits a perfect matching; in the case where the graph has a perfect...
A perfect matching in a k-uniform hypergraph on n vertices, n divisible by k, is a set of n/k disjoint edges. In this paper we give a sufficient condition for the existence of a p...
We develop a new form of reweighting (Wainwright et al., 2005b) to leverage the relationship between Ising spin glasses and perfect matchings into a novel technique for the exact ...