Abstract
We present recent results regarding rainbow matchings in bipartite graphs. Using topological methods we address a known conjecture of Stein and show that if Kn,n is partitioned into n sets of size n, then a partial rainbow matching of size 2n/3 exists. We generalize a result of Cameron and Wanless and show that for any n matchings of size n in a bipartite graph with 2n vertices there exists a full matching intersecting each matching at most twice. We show that any n matchings of size approximately 3n/2 have a rainbow matching of size n. Finally, we show the uniqueness of the extreme case for a theorem of Drisko and provide a generalization of Drisko's theorem.
Original language | English |
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Pages (from-to) | 479-484 |
Number of pages | 6 |
Journal | Electronic Notes in Discrete Mathematics |
Volume | 63 |
DOIs | |
State | Published - Dec 2017 |
Bibliographical note
Publisher Copyright:© 2017 Elsevier B.V.
Keywords
- Ryser-Brualdi Conjecture
- Stein's conjecture
- bipartite graph
- full rainbow matching
- partial rainbow matching
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics