Forte Shinko

Randomized Borel $(2d+1)$-coloring of digraphs

Let $G$ be a Borel digraph with maximum out-degree $d \in \mathbb{N}$. We show that $G$ admits a random Borel $(2d+1)$-coloring for which every edge is almost surely not monochromatic. This gives a simpler proof of a recent result of Pelayo-G\'omez: such a graph $G$ admits a measurable proper $(2d+1)$-coloring with res...