Optimal $\chi$-boundness of $\ell$-holed graphs

Yan Wang; Rong Wu

Optimal $\chi$-boundness of $\ell$-holed graphs

Combinatorics 2025-08-12 v1

Authors: Yan Wang , Rong Wu

Abstract

A graph is {\em{ $\ell$ -holed}} if all of its induced cycles of length at least four have length exactly $\ell$ . In the paper, we prove that if $G$ is an $\ell$ -holed graph with odd $\ell\geq 7$ , then $\chi(G)\leq {\lceil {\ell \over {\ell-1}}\omega(G) \rceil}$ . This result is sharp.

Keywords

graph cycles graph pebbling graph theory

Cite

@article{arxiv.2508.07034,
  title  = {Optimal $\chi$-boundness of $\ell$-holed graphs},
  author = {Yan Wang and Rong Wu},
  journal= {arXiv preprint arXiv:2508.07034},
  year   = {2025}
}

Comments

arXiv admin note: text overlap with arXiv:2110.09970, arXiv:2410.19005 by other authors

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