Vertex partitions of [formula omitted]-free planar graphs

Abstract

A graph is (k1,k2)-colorable if it admits a vertex partition into a graph with maximum degree at most k1 and a graph with maximum degree at most k2. We show that every (C3,C4,C6)-free planar graph is (0,6)-colorable. We also show that deciding whether a (C3,C4,C6)-free planar graph is (0,3)-colorable is NP-complete.