论文标题
（p_5，hvn）的色数 - 免费图
The chromatic number of (P_5, HVN )-free graphs
论文作者
论文摘要
令$ g $为图。我们使用$χ（g）$和$ω（g）$分别表示$ g $的色数和集团数。 $ p_5 $是5个顶点的路径，而$ hvn $是$ k_4 $，还有另一个顶点，恰好与两个$ k_4 $的顶点相邻。结合一些已知结果，在本文中，我们表明，如果$ g $为$（p_5，\ textit {hvn}）$ - 免费，则$χ（g）\ leq \ leq \ max \ {\ min \ {\ min \ {16，ω（g）+3 \}，+3 \}，ω（g）+1 \ \} $。这种上限几乎是锋利的。
Let $G$ be a graph. We use $χ(G)$ and $ω(G)$ 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 $χ(G)\leq \max\{\min\{16, ω(G)+3\}, ω(G)+1\}$. This upper bound is almost sharp.
