Equitable list coloring of planar graphs without 4- and 6-cycles

A graph GG is equitably kk-choosable if for any kk-uniform list assignment LL, there exists an LL-colorable of GG such that each color appears on at most ⌈|V(G)|k⌉ vertices. Kostochka, Pelsmajer and West introduced this notion and conjectured that GG is equitably kk-choosable for k>Δ(G)k>Δ(G). We prove this for planar graphs with Δ(G)≥6Δ(G)≥6 and no 4- or 6-cycles.