$4$-choosability of planar graphs with $4$-cycles far apart via the Combinatorial Nullstellensatz

Fan Yang, Yue Wang, Jian-liang Wu

By a well-known theorem of Thomassen and a planar graph depicted by Voigt, we know that every planar graph is $5$-choosable, and the bound is tight. In 1999, Lam, Xu and Liu reduce…