论文标题
（$ p_ {5}，k_ {5} -e $）的色数 - 免费图
The chromatic number of ($P_{5}, K_{5}-e$)-free graphs
论文作者
论文摘要
令$ 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 $是5个顶点的路径。如果存在某些函数$ f $，则图$ \ MATHCAL {G} $被称为{\ IT $χ$ bounded}，以便每个$ f（g）\ leq f（ω（g））对于每个$ g \ in \ Mathcal {g} $。在本文中，我们表明$（p_5，k_5-e）$的家族是由线性函数结合的$χ$ - $χ（g）\ leq \ max \ max \ {13，ω（g）+1 \} $。
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. A family of graphs $\mathcal{G}$ is said to be {\it$χ$-bounded} if there exists some function $f$ such that $χ(G)\leq f(ω(G))$ for every $G\in\mathcal{G}$. In this paper, we show that the family of $(P_5, K_5-e)$-free graphs is $χ$-bounded by a linear function: $χ(G)\leq \max\{13,ω(G)+1\}$.
