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The Multicolour Size--Ramsey Number of an Even Cycle
Abstract
We determine the k-colour size--Ramsey number of even cycles up to absolute constant factors. For every k≥2 and every even n≥100log k, R̂k(Cn)=Θ(k2log k)n. The lower bound follows from the corresponding result of Beke, Li and Sahasrabudhe for paths, while our upper bound improves the previous best estimate O(k34n) of Javadi, Kohayakawa and Miralaei.
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BibTeX
@misc{wang2026multicolour,
title = {{The Multicolour Size--Ramsey Number of an Even Cycle}},
author = {Lanchao Wang and Xiaolin Wang},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30481},
eprint = {2608.30481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30481},
}
RIS
TY - UNPB
TI - The Multicolour Size--Ramsey Number of an Even Cycle
AU - Lanchao Wang
AU - Xiaolin Wang
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30481
UR - https://arxiv.org/abs/2608.30481
AB - We determine the k-colour size--Ramsey number of even cycles up to absolute constant factors. For every k≥2 and every even n≥100log k, R̂_k(C_n)=Θ(k^2log k)n. The lower bound follows from the corresponding result of Beke, Li and Sahasrabudhe for paths, while our upper bound improves the previous best estimate O(k^34n) of Javadi, Kohayakawa and Miralaei.
ER -