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

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 reduced 5 to 4 on C 4 -free planar graphs. In the paper, by applying the famous Combinatorial Nullstellensatz, we design an effective algorithm to deal with list coloring problems. At the same time, we prove that a planar graph G is 4-choosable if any two 4-cycles having distance at least 5 in G , which extends the result of Lam et al. [ABSTRACT FROM AUTHOR]