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- W4377372103 abstract "Finding families that admit a linear $chi$-binding function is a problem that has interested researchers for a long time. Recently, the question of finding linear subfamilies of $2K_2$-free graphs has garnered much attention. In this paper, we are interested in finding a linear subfamily of a specific superclass of $2K_2$-free graphs, namely $(P_3cup P_2)$-free graphs. We show that the class of ${P_3cup P_2,gem}$-free graphs admits $f=2omega$ as a linear $chi$-binding function. Furthermore, we give examples to show that the optimal $chi$-binding function $f^*geq leftlceilfrac{5omega(G)}{4}rightrceil$ for the class of ${P_3cup P_2, gem}$-free graphs and that the $chi$-binding function $f=2omega$ is tight when $omega=2$ and $3$." @default.
- W4377372103 created "2023-05-23" @default.
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- W4377372103 date "2023-05-19" @default.
- W4377372103 modified "2023-09-29" @default.
- W4377372103 title "Linear $chi$-binding functions for ${P_3cup P_2, gem}$-free graphs" @default.
- W4377372103 doi "https://doi.org/10.48550/arxiv.2305.11757" @default.
- W4377372103 hasPublicationYear "2023" @default.
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