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Proceedings of the American Mathematical Society

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Locally planar toroidal graphs are $ 5$-colorable

Authors: Michael O. Albertson and Walter R. Stromquist
Journal: Proc. Amer. Math. Soc. 84 (1982), 449-457
MSC: Primary 05C10; Secondary 05C15
MathSciNet review: 640251
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Abstract: If a graph can be embedded in a torus in such a way that all noncontractible cycles have length at least 8, then its vertices may be $ 5$-colored. The conclusion remains true when some noncontractible cycles have length less than 8, if the exceptions are all homotopic. Essentially this hypothesis means that small neighborhoods of the graph are planar. No similar conclusion holds for $ 4$-colorability.

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Keywords: Toroidal graph, vertex coloring
Article copyright: © Copyright 1982 American Mathematical Society

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