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Planar graphs are 1-relaxed, 4-choosable. (English) Zbl 1221.05077
Summary: We show that every planar graph $$G=(V,E)$$ is 1-relaxed, 4-choosable. This means that, for every list assignment $$L$$ that assigns a set of at least four colors to each vertex, there exists a coloring $$f$$ such that $$f(v)\in L(v)$$ for every vertex $$v\in V$$ and each color class $$f^{ - 1}(\alpha )$$ of $$f$$ induces a subgraph with maximum degree at most 1.

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