Equitable Choosability of Prism Graphs

Abstract

A graph $G$ is equitably $k$-choosable if, for every $k$-uniform list assignment $L$, $G$ is $L$-colorable and each color appears on at most $\left\lceil |V(G)|/k\right\rceil$ vertices. Equitable list-coloring was introduced by Kostochka, Pelsmajer, and West in 2003. They conjectured that a connected graph $G$ with $\Delta(G)\geq 3$ is equitably $\Delta(G)$-choosable, as long as $G$ is not complete or $K_{d,d}$ for odd $d$. In this paper, we use a discharging argument to prove their conjecture for the infinite family of prism graphs.