On a conjecture of Stein

Ron Aharoni, Eli Berger, Dani Kotlar, Ran Ziv

Research output: Contribution to journalArticlepeer-review

Abstract

Stein (Pac J Math 59:567–575, 1975) proposed the following conjecture: if the edge set of Kn , n is partitioned into n sets, each of size n, then there is a partial rainbow matching of size n- 1. He proved that there is a partial rainbow matching of size n(1-Dnn!), where Dn is the number of derangements of [n]. This means that there is a partial rainbow matching of size about (1-1e)n. Using a topological version of Hall’s theorem we improve this bound to 23n.

Original languageEnglish
Pages (from-to)203-211
Number of pages9
JournalAbhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume87
Issue number2
DOIs
StatePublished - 1 Oct 2017

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).

Keywords

  • Rainbow matchings
  • Ryser’s Latin Square conjecture
  • Transversals

ASJC Scopus subject areas

  • Mathematics (all)

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