Equitable Choosability of Prism Graphs

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.