On odd rainbow cycles in edge-colored graphs

Andrzej Czygrinow, Theodore Molla, Brendan Nagle, Roy Oursler

Research output: Contribution to journalArticlepeer-review

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 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 languageEnglish (US)
Article number103316
JournalEuropean Journal of Combinatorics
Volume94
DOIs
StatePublished - May 2021
Externally publishedYes

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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