Abstract
A conjecture of the first two authors is that n matchings of size n in any graph have a rainbow matching of size n−1. We prove a lower bound of23n−1, improving on the trivial12n, and an analogous result for hypergraphs. For{C3, C5}-free graphs and for disjoint matchings we obtain a lower bound of3n4 − O(1). We also discuss a conjecture on rainbow alternating paths, that if true would yield a lower bound of n −√2n. We prove the non-alternating (ordinary paths) version of this conjecture.
| Original language | English |
|---|---|
| Article number | P1.10 |
| Journal | Electronic Journal of Combinatorics |
| Volume | 29 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2022 |
Bibliographical note
Funding Information:∗We acknowledge the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no. 075-15-2019-1926 when the first author worked on Section 3 of the paper. The research of R. Aharoni was supported in part by the Israel Science Foundation (ISF) grant no. 2023464 and the Discount Bank Chair at the Technion. This paper is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skldowska-Curie grant agreement no. 823748. †Supported by NSF Grant DMS-1763817.
Funding Information:
‡Supported by NSF grant DMS-1953929. The authors were supported by US-Israel Binational Science Foundation (BSF) grant no. 2016077.
Publisher Copyright:
© The authors.
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics