BROOKS’ THEOREM FOR MEASURABLE COLORINGS
BROOKS’ THEOREM FOR MEASURABLE COLORINGS
We generalize Brooks’ theorem to show that if $G$ is a Borel graph on a standard Borel space $X$ of degree bounded by $d\geqslant 3$ which contains no $(d+1)$ -cliques, then $G$ admits a ${\it\mu}$ -measurable $d$ -coloring with respect to any Borel probability measure ${\it\mu}$ on $X$ , and …