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Vertex partitions of $$(C_3, C_4, C_6)$$-free planar graphs. (English) Zbl 1419.05053
Summary: A graph is $$(k_1, k_2)$$-colorable if it admits a vertex partition into a graph with maximum degree at most $$k_1$$ and a graph with maximum degree at most $$k_2$$. We show that every $$(C_3, C_4, C_6)$$-free planar graph is $$(0, 6)$$-colorable. We also show that deciding whether a $$(C_3, C_4, C_6)$$-free planar graph is $$(0, 3)$$-colorable is NP-complete.
##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C15 Coloring of graphs and hypergraphs 68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
##### Keywords:
improper colorings; planar graphs
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##### References:
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