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Proceedings of the American Mathematical Society

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A $ 4$-color theorem for toroidal graphs


Authors: Hudson V. Kronk and Arthur T. White
Journal: Proc. Amer. Math. Soc. 34 (1972), 83-86
MSC: Primary 05C15
MathSciNet review: 0291019
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Abstract: It is well known that any graph imbedded in the torus has chromatic number at most seven, and that seven is attained by the graph $ {K_7}$. In this note we show that any toroidal graph containing no triangles has chromatic number at most four, and produce an example attaining this upper bound. The results are then extended for arbitrary girth.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291019-5
Keywords: Graph, chromatic number, torus, girth
Article copyright: © Copyright 1972 American Mathematical Society