TY - JOUR
T1 - On odd rainbow cycles in edge-colored graphs
AU - Czygrinow, Andrzej
AU - Molla, Theodore
AU - Nagle, Brendan
AU - Oursler, Roy
N1 - Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/5
Y1 - 2021/5
N2 - 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 Cℓ 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.
AB - 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 Cℓ 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.
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U2 - 10.1016/j.ejc.2021.103316
DO - 10.1016/j.ejc.2021.103316
M3 - Article
AN - SCOPUS:85101108196
SN - 0195-6698
VL - 94
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103316
ER -