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.
|Number of pages||9|
|Journal||Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg|
|State||Published - 1 Oct 2017|
Bibliographical notePublisher Copyright:
© 2016, The Author(s).
- Rainbow matchings
- Ryser’s Latin Square conjecture
ASJC Scopus subject areas
- Mathematics (all)