For a graph $G$, let $\chi(G)$ ($\omega(G)$) denote its chromatic (clique) number. A $P_2+P_3$ is the graph obtained by taking the disjoint union of a two-vertex path $P_2$ and a three-vertex path $P_3$. A $\bar{P_2+P_3}$ is the complement graph of a $P_2+P_3$. In this paper, we study the class of ($P_2+P_3$, $\bar{P_2+P_3}$)-free graphs and show that every such graph $G$ with $\omega(G)\geq 3$ satisfies $\chi(G)\leq \max \{\omega(G)+3, \lfloor\frac{3}{2} \omega(G) \rfloor-1 \}$. Moreover, the bound is tight. Indeed, for any $k\in {\mathbb N}$ and $k\geq 3$, there is a ($P_2+P_3$, $\bar{P_2+P_3}$)-free graph $G$ such that $\omega(G)=k$ and $\chi(G)=\max\{k+3, \lfloor\frac{3}{2} k \rfloor-1 \}$.

翻译：$\bar{P_2+P_3} 对于一个G$的图形, 请让$\chi( G) $ (G) 表示它的色( clique) 。 A$_ 2+P_ 3$ 是使用两个顶端路径的脱节 $P_ 2美元和三个顶端路径 $P_ 3美元获得的图表。 A$\bar{ P_ 2+P_ 3} 是一个底层 { P_ 2+P_ 3$ 的补充图 。 在本文中, 我们研究的是$( 2+P_ 3美元 $ 。 $\ 2+ P_ 3} 无色图表, 并显示每张G$\ g$\ leq\ $\ leq =max ⁇ = omega( G) + 3, = g$( G) (G) +_ $( $) 美元和 美元 美元。 此外, 约束很紧。 事实上, 对于任何美元 $- g$$_ g$$__ g$_ g$_ $_ g_ a, $_ g_ a_