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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A three and five color theorem
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by Frank R. Bernhart PDF
Proc. Amer. Math. Soc. 52 (1975), 493-498 Request permission

Abstract:

Let $f$ be a face of a plane graph $G$. The Three and Five Color Theorem proved here states that the vertices of $G$ can be colored with five colors, and using at most three colors on the boundary of $f$. With this result the well-known Five Color Theorem for planar graphs can be strengthened, and a relative coloring conjecture of Kainen can be settled except for a single case which happens to be a paraphrase of the Four Color Conjecture. Some conjectures are presented which are intermediate in strength to the Four Color Conjecture and the Three and Five Color Theorem.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 52 (1975), 493-498
  • MSC: Primary 05C15
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0373944-2
  • MathSciNet review: 0373944