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

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