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arXiv · 2102.13458

Chromatic bounds for the subclasses of $pK_2$-free graphs

Athmakoori Prashant·S. Francis Raj·M. Gokulnath
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Abstract

The concept of $\chi$-binding functions for classes of free graphs has been extensively studied in the past. In this paper, we improve the existing $\chi$-binding function for $\{2K_2, K_1 + C_4\}$-free graphs. Also, we find a linear $\chi$-binding function for $\{2K_2, K_2+P_4\}$-free graphs. In addition, we give alternative proofs for the $\chi$-binding function of $\{2K_2,gem\}$-free graphs, $\{2K_2,HVN\}$-free graphs and $\{2K_2, K_5-e\}$-free graphs. Finally, for $p\geq3$, we find polynomial $\chi$-binding functions for $\{pK_2, H\}$-free graphs where $H\in \{gem, diamond, K_2+P_4, HVN, K_5-e, butterfly, gem^+, dart, K_1 + C_4, C_4, \overline{P_5}\}$.

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Athmakoori Prashant, S. Francis Raj, M. Gokulnath. 2021-02-26. Chromatic bounds for the subclasses of $pK_2$-free graphs. https://arxiv.org/abs/2102.13458

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