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A 4-Color Theorem for Toroidal Graphs

Hudson V. Kronk and Arthur T. White
Proceedings of the American Mathematical Society
Vol. 34, No. 1 (Jul., 1972), pp. 83-86
DOI: 10.2307/2037902
Stable URL: http://www.jstor.org/stable/2037902
Page Count: 4
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A 4-Color Theorem for Toroidal Graphs
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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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