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

Ran Chen, Di Wu, Xiaowen Zhang

The Borodin-Kostochka Conjecture states that for a graph $G$, if $\Delta (G)\ge 9$, then $\chi (G)\le \max \{\Delta (G)-1,\omega (G)\}$. We use $P_t$ and $C_t$ to denote a path and a cycle on $t$ vertice…