THE EQUITABLE CHROMATIC THRESHOLD OF THE CARTESIAN PRODUCT OF BIPARTITE GRAPHS IS AT MOST 4
Zhidan Yan, Wu-Hsiung Lin, Wei Wang · Taiwanese Journal of Mathematics · 2014
A graph $G$ is equitably $k$-colorable if its vertex set can be partitioned into $k$ independent sets, any two of which differ in size by at most 1. We prove a conjecture of Lin and Chang which asserts that for any bipartite graphs $G$ and $H$, their Cartesian product $G\Box H$ is equitably $k$-colorable whenever $k\ge 4$.