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A graph is $(k_1,k_2)$-colorable if its vertex set can be partitioned into agraph with maximum degree at most $k_1$ and and a graph with maximum degree atmost $k_2$. We show that every $(C_3,C_4,C_6)$-free planar graph is$(0,6)$-colorable. We also show that deciding whether a $(C_3,C_4,C_6)$-freeplanar graph is $(0,3)$-colorable is NP-complete.

Vertex partitions of $(C_3,C_4,C_6)$-free planar graphs