Mathematics > Combinatorics
[Submitted on 13 Apr 2022 (v1), last revised 26 Aug 2022 (this version, v4)]
Title:The chromatic number of (P_5, HVN )-free graphs
View PDFAbstract:Let $G$ be a graph. We use $\chi(G)$ and $\omega(G)$ to denote the chromatic number and clique number of $G$ respectively. A $P_5$ is a path on 5 vertices, and an $HVN$ is a $K_4$ together with one more vertex which is adjacent to exactly two vertices of $K_4$. Combining with some known result, in this paper we show that if $G$ is $(P_5, \textit{HVN})$-free, then $\chi(G)\leq \max\{\min\{16, \omega(G)+3\}, \omega(G)+1\}$. This upper bound is almost sharp.
Submission history
From: Yian Xu Dr. [view email][v1] Wed, 13 Apr 2022 15:32:12 UTC (93 KB)
[v2] Sun, 1 May 2022 04:00:10 UTC (95 KB)
[v3] Fri, 29 Jul 2022 10:26:07 UTC (95 KB)
[v4] Fri, 26 Aug 2022 03:37:37 UTC (95 KB)
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