On the Existence of Zero-Sum Perfect Matchings of Complete Graphs
Combinatorics
2020-11-03 v1
Abstract
In this paper, we prove that given a 2-edge-coloured complete graph that has the same number of edges of each colour, we can always find a perfect matching with an equal number of edges of each colour. This solves a problem posed by Caro, Hansberg, Lauri, and Zarb. The problem is also independently solved by Ehard, Mohr, and Rautenbach.
Cite
@article{arxiv.2011.00862,
title = {On the Existence of Zero-Sum Perfect Matchings of Complete Graphs},
author = {Teeradej Kittipassorn and Panon Sinsap},
journal= {arXiv preprint arXiv:2011.00862},
year = {2020}
}
Comments
12 pages, 6 figures, 3 tables, submitted