TY - JOUR
T1 - On odd rainbow cycles in edge-colored graphs
AU - Czygrinow, Andrzej
AU - Molla, Theodore
AU - Nagle, Brendan
AU - Oursler, Roy
N1 - Funding Information:
The first author was partially supported by Simons Foundation, USA Grant #521777.The second author was partially supported by National Science Foundation, USA Grants DMS 1500121 and DMS 1800761.The third author was partially supported by National Science Foundation, USA Grant DMS 1700280.
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
VL - 94
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
M1 - 103316
ER -