# Rainbow matchings in properly-coloured multigraphs

Keevash, P
Yepremyan, L

10 July 2018

## Journal:

SIAM Journal on Discrete Mathematics

## Last Updated:

2020-05-09T23:40:46.817+01:00

3

32

## DOI:

10.1137/17M1151742

1577-1584

## abstract:

Aharoni and Berger conjectured that in any bipartite multigraph that is properly edge-coloured by $n$ colours with at least $n + 1$ edges of each colour there must be a matching that uses each colour exactly once. In this paper we consider the same question without the bipartiteness assumption. We show that in any multigraph with edge multiplicities $o(n)$ that is properly edge-coloured by $n$ colours with at least $n + o(n)$ edges of each colour there must be a matching of size $n-O(1)$ that uses each colour at most once.

735439

Submitted

Journal Article