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Anti-Ramsey Number of Intersecting Odd Cycles
Abstract
For a graph H, the anti-Ramsey number ar(n,H) is the maximum number of colors in an edge-coloring of Kn containing no rainbow copy of H, where a copy is rainbow if its edges have pairwise distinct colors. Let s,t be nonnegative integers with s+t≥2, and let Hs,t be a graph consisting of s triangles and t odd cycles of fixed lengths at least $5$, all sharing exactly one common vertex and otherwise pairwise vertex-disjoint. Liu et al. (2024) determined ar(n,Hs,0) for s≥3 and n≥50s2. In this paper, we determine the exact value of ar(n,Hs,t) for every fixed Hs,t with t≥1 and all sufficiently large n.
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BibTeX
@misc{zheng2026antiramsey,
title = {{Anti-Ramsey Number of Intersecting Odd Cycles}},
author = {Haojie Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32151},
eprint = {2609.32151},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32151},
}
RIS
TY - UNPB
TI - Anti-Ramsey Number of Intersecting Odd Cycles
AU - Haojie Zheng
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32151
UR - https://arxiv.org/abs/2609.32151
AB - For a graph H, the anti-Ramsey number ar(n,H) is the maximum number of colors in an edge-coloring of K_n containing no rainbow copy of H, where a copy is rainbow if its edges have pairwise distinct colors. Let s,t be nonnegative integers with s+t≥2, and let H_s,t be a graph consisting of s triangles and t odd cycles of fixed lengths at least $5$, all sharing exactly one common vertex and otherwise pairwise vertex-disjoint. Liu et al. (2024) determined ar(n,H_s,0) for s≥3 and n≥50s^2. In this paper, we determine the exact value of ar(n,H_s,t) for every fixed H_s,t with t≥1 and all sufficiently large n.
ER -