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It is known that for every $(P_3\\cup P_2)$-free graph $G$, $\\chi(G)\\le \\frac{1}{6}\\omega(G)(\\omega(G)+1)(\\omega(G)+2)$ \\cite{BA18}, and the class of $(2K_2, 3K_1)$-free graphs does not admit a linear $\\chi$-binding function\\cite{BBS19}. 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