Coloring $(P_6,C_4)$-free graphs with $\Delta -1$ colors

Uttam K. Gupta, Dinabandhu Pradhan, Rashmi Rekha Swain

For a graph $G$, let $\Delta (G)$, $\omega (G)$, and $\chi (G)$ denote the maximum degree, clique number, and chromatic number of $G$, respectively. Let $P_n$ and $C_n$ denote the chordless path a…