Planar graphs without 4-cycles adjacent to 3-cycles are list vertex 2-arborable.

*(English)*Zbl 1180.05035Authors’ 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.”

Reviewer: Saul Stahl (Lawrence)

##### MSC:

05C10 | Planar graphs; geometric and topological aspects of graph theory |

05C15 | Coloring of graphs and hypergraphs |

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\textit{O. V. Borodin} and \textit{A. O. Ivanova}, J. Graph Theory 62, No. 3, 234--240 (2009; Zbl 1180.05035)

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