Athmakoori Prashant, S. Francis Raj, M. Gokulnath
Published 2021-02-26Version 1
In this paper, we study the chromatic number for graphs with forbidden induced subgraphs. We improve the existing $\chi$-binding functions for some subclasses of $2K_2$-free graphs, namely $\{2K_2, H\}$-free graphs where $H\in \{K_5-e, K_2+P_4, K_1 + C_4\}$. In addition, for $p\geq3$, we find the polynomial $\chi$-binding functions $\{pK_2, H\}$-free graphs where $H\in \{gem, diamond, HVN, K_5-e, K_2+P_4, butterfly, dart, gem^+, C_4, K_1 + C_4, \overline{P_5}\}$.
Coloring $(P_5, \text{gem})$-free graphs with $Δ-1$ colors
A note on Hadwiger's Conjecture for $W_5$-free graphs with independence number two
Polynomial $χ$-binding functions for $t$-broom-free graphs
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