Full rainbow matchings in graphs and hypergraphs

Pu Gao, Reshma Ramadurai, Ian M. Wanless, Nick Wormald

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Let G be a simple graph that is properly edge-coloured with m colours and let be the set of m matchings induced by the colours in G. Suppose that, where 9/10\]]]>, and every matching in has size n. Then G contains a full rainbow matching, i.e. a matching that contains exactly one edge from Mi for each. This answers an open problem of Pokrovskiy and gives an affirmative answer to a generalization of a special case of a conjecture of Aharoni and Berger. Related results are also found for multigraphs with edges of bounded multiplicity, and for hypergraphs. Finally, we provide counterexamples to several conjectures on full rainbow matchings made by Aharoni and Berger.

Original languageEnglish
Pages (from-to)762-780
Number of pages19
JournalCombinatorics, Probability and Computing
Volume30
Issue number5
DOIs
Publication statusPublished - Sep 2021

Keywords

  • 05C70
  • 05D15
  • 2020 MSC Codes:

Cite this