We consider the following question: given an (X,Y)-bigraph G and a set S⊂X, does G contain two disjoint matchings M1 and M2 such that M1 saturates X and M2 saturates S? When ∣S∣≥∣X∣−1, this question is solvable by finding an appropriate factor of the graph. In contrast, we show that when S is allowed to be an arbitrary subset of X, the problem is NP-hard.
@article{arxiv.1506.06157,
title = {Complexity of a Disjoint Matching Problem on Bipartite Graphs},
author = {Gregory J. Puleo},
journal= {arXiv preprint arXiv:1506.06157},
year = {2015}
}