论文标题
$χ$ - 结合功能的某些类别的$（P_3 \ CUP P_2）$ - 免费图形
$χ$-binding functions for some classes of $(P_3\cup P_2)$-free graphs
论文作者
论文摘要
过去在各种情况下，$ 2K_2 $的$ 2 $ - 免费图表都经过了很好的研究。众所周知，$ \ {2k_2,2k_1+k_p \} $ - 免费图形和$ \ {2k_2，（k_1 \ cup k_2）+k_p \} $ - 免费图形 - 接收图形，接收一个线性$χ$ - 结合功能。在本文中，我们研究$（P_3 \ CUP P_2）$的类别 - 免费图形，这是$ 2K_2 $ - 免费图形的超类。我们表明$ \ {p_3 \ cup p_2,2k_1+k_p \} $ - 免费图形和$ \ {p_3 \ cup p_2，（k_1 \ cup k_2）+k_2）+k_p \} $ - 免费的图形也承认，也承认linear $ cub $χ$χ$ - binding功能。 In addition, we give tight chromatic bounds for $\{P_3\cup P_2,HVN\}$-free graphs and $\{P_3\cup P_2,diamond\}$-free graphs and it can be seen that the latter is an improvement of the existing bound given by A. P. Bharathi and S. A. Choudum [Colouring of $(P_3\cup P_2)$-free图，图和组合学34（2018），97-107]。
The class of $2K_2$-free graphs have been well studied in various contexts in the past. It is known that the class of $\{2K_2,2K_1+K_p\}$-free graphs and $\{2K_2,(K_1\cup K_2)+K_p\}$-free graphs admits a linear $χ$-binding function. In this paper, we study the classes of $(P_3\cup P_2)$-free graphs which is a superclass of $2K_2$-free graphs. We show that $\{P_3\cup P_2,2K_1+K_p\}$-free graphs and $\{P_3\cup P_2,(K_1\cup K_2)+K_p\}$-free graphs also admits linear $χ$-binding functions. In addition, we give tight chromatic bounds for $\{P_3\cup P_2,HVN\}$-free graphs and $\{P_3\cup P_2,diamond\}$-free graphs and it can be seen that the latter is an improvement of the existing bound given by A. P. Bharathi and S. A. Choudum [Colouring of $(P_3\cup P_2)$-free graphs, Graphs and Combinatorics 34 (2018), 97-107].
