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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2037902
Page Count: 4
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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.
Proceedings of the American Mathematical Society © 1972 American Mathematical Society