On Edge-Disjoint Pairs Of Matchings
V. V. Mkrtchyan, V. L. Musoyan, A. V. Tserunyan
TL;DR
This paper investigates the maximum size of edge-disjoint matching pairs in a graph, establishing a tight upper bound of 5/4 for the ratio of the maximum matching to the largest matching in such pairs.
Contribution
It introduces a precise bound on the ratio of maximum matchings to matchings in edge-disjoint pairs, advancing understanding of matchings in graph theory.
Findings
The ratio |M|/|H| is at most 5/4.
The bound of 5/4 is tight.
Provides new insights into the structure of edge-disjoint matchings.
Abstract
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|.
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