On odd rainbow cycles in edge-colored graphs. (May 2021)

• Record Type: Journal Article
• Authors: Czygrinow, Andrzej; Molla, Theodore; Nagle, Brendan; Oursler, Roy
• Is Part Of: European journal of combinatorics. Volume 94(2021)
• Publication Date: 2021-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2021.103316
• Languages: English
• ISSNs: 0195-6698

Abstract

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 ≥ 432 ℓ . This result is sharp for all odd integers ℓ ≥ 3, and extends earlier work of the authors for when ℓ is even.