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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0640251-3
PII: S 0002-9939(1982)0640251-3
Keywords: Toroidal graph, vertex coloring
Article copyright: © Copyright 1982 American Mathematical Society