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On 3-choosability of plane graphs having no 3-, 6-, 7- and 8-cycles. (English) Zbl 1177.05042

Summary: A graph is \(k\)-choosable if it can be colored whenever every vertex has a list of available colors of size at least \(k\). It is a generalization of graph coloring where all vertices do not have the same available colors. We show that every traingle-free plane graph without 6-, 7- and 8-cycles is 3-choosable.

MSC:

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