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Planar graphs without 3-,7-, and 8-cycles are 3-choosable
Dvořák, Zdeněk ; Lidický, Bernard ; Škrekovski, Riste
A graph is ▫$k$▫-choosable if it can be colored whenever every vertex has a list of available colors of size at least k. Grötzsch's theorem states that every planar triangle-free graph is ...3-colorable. However, Voigt gave an example of such a graph that is not 3-choosable, thus Grötzsch's theorem does not generalize naturally to choosability. We prove that every planar triangle-free graph without 7- and 8- cycles is 3-choosable.
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