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Planar graphs without cycles of length 4, 7, 8, or 9 are 3-choosable. (English) Zbl 1210.05029
Summary: It is known that planar graphs without cycles of length 4, $$i, j$$, or 9 with $$4<i<j<9$$, except that $$i=7$$ and $$j=8$$, are 3-choosable. This paper proves that planar graphs without cycles of length 4, 7, 8, or 9 are also 3-choosable.

##### MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C38 Paths and cycles 05C15 Coloring of graphs and hypergraphs
##### Keywords:
planar graph; cycle; choosability; coloring
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##### References:
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