A Note on List Improper Coloring Planar Graphs

Abstract

Communicated by R. L. Grahm Abstract--A graph G is called (k, d)*-choosable if, for every list assignment L satisfying [L(v)l = k for all v E V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles an