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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.)
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