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Planar graphs without 4-cycles adjacent to 3-cycles are list vertex 2-arborable. (English) Zbl 1180.05035
Authors’ summary: “It is known that not all planar graphs are 4-choosable; neither all of them are vertex 2-arborable. However, planar graphs without 4-cycles and even those without 4-cycles adjacent to 3-cycles are known to be 4-choosable. We extend this last result in terms of covering the vertices of a graph by induced subgraphs of variable degeneracy. In particular, we prove that every planar graph without 4-cycles adjacent to 3-cycles can be covered by two induced forests.”

MSC:
05C10 Planar graphs; geometric and topological aspects of graph theory
05C15 Coloring of graphs and hypergraphs
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