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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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