A $4$-color theorem for toroidal graphs
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- by Hudson V. Kronk and Arthur T. White
- Proc. Amer. Math. Soc. 34 (1972), 83-86
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291019-5
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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.References
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Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 83-86
- MSC: Primary 05C15
- DOI: https://doi.org/10.1090/S0002-9939-1972-0291019-5
- MathSciNet review: 0291019