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 language | English |
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Pages (from-to) | 203-211 |
Number of pages | 9 |
Journal | Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg |
Volume | 87 |
Issue number | 2 |
DOIs | |
State | Published - 1 Oct 2017 |
Bibliographical note
Publisher Copyright:© 2016, The Author(s).
Keywords
- Rainbow matchings
- Ryser’s Latin Square conjecture
- Transversals
ASJC Scopus subject areas
- General Mathematics