For a graph G, consider the pairs of edge-disjoint matchings whose union consists of as many edges as possible. Let H be the largest matching among such pairs. Let M be a maximum matching of G. We show that 5/4 is a tight upper bound for |M|/|H|.
@article{arxiv.0708.1903,
title = {On Edge-Disjoint Pairs Of Matchings},
author = {V. V. Mkrtchyan and V. L. Musoyan and A. V. Tserunyan},
journal= {arXiv preprint arXiv:0708.1903},
year = {2008}
}
Comments
8 pages, 2 figures, Submitted to Discrete Mathematics