Borodin-Kostochka Conjecture holds for odd-hole-free graphs

Abstract

The Borodin-Kostochka Conjecture states that for a graph $G$, if $\Delta (G)\ge 9$, then $\chi (G)\le \max \{\Delta (G)-1,\omega (G)\}$. In this paper, we prove the Borodin-Kostochka Conjecture holding for odd-hole-free graphs.

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