On odd rainbow cycles in edge-colored graphs

Andrzej Czygrinow; Theodore Molla; Brendan Nagle; Roy Oursler

doi:10.1016/j.ejc.2021.103316

On odd rainbow cycles in edge-colored graphs

Andrzej Czygrinow, Theodore Molla, Brendan Nagle, Roy Oursler

Mathematical and Statistical Sciences, School of (SoMSS)

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

6 Scopus citations

Abstract

Let G=(V,E) be an n-vertex edge-colored graph. In 2013, H. Li proved that if every vertex v∈V is incident to at least (n+1)∕2 distinctly colored edges, then G admits a rainbow triangle. We prove that the same hypothesis ensures a rainbow ℓ-cycle C_ℓ whenever n≥432ℓ. This result is sharp for all odd integers ℓ≥3, and extends earlier work of the authors for when ℓ is even.

Original language	English (US)
Article number	103316
Journal	European Journal of Combinatorics
Volume	94
DOIs	https://doi.org/10.1016/j.ejc.2021.103316
State	Published - May 2021

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2021.103316

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AU - Nagle, Brendan

AU - Oursler, Roy

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On odd rainbow cycles in edge-colored graphs

Abstract

ASJC Scopus subject areas

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