Rainbow paths and large rainbow matchings

Ron Aharoni; Eli Berger; Maria Chudnovsky; Shira Zerbib

doi:10.37236/10173

Rainbow paths and large rainbow matchings

Ron Aharoni, Eli Berger, Maria Chudnovsky, Shira Zerbib

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.37236/10173
State	Published - 2022

Bibliographical note

Publisher Copyright:
© The authors.

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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Rainbow paths and large rainbow matchings

Abstract

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