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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Even triangulations of $ S\sp{3}$ and the coloring of graphs


Authors: Jacob Eli Goodman and Hironori Onishi
Journal: Trans. Amer. Math. Soc. 246 (1978), 501-510
MSC: Primary 05C15; Secondary 57M15
DOI: https://doi.org/10.1090/S0002-9947-1978-0515556-0
MathSciNet review: 515556
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Abstract: A simple necessary and sufficient condition is given for the vertices of a graph, planar or not, to be properly four-colorable. This criterion involves the notion of an ``even'' triangulation of $ {S^3}$ and generalizes, in a natural way, a corresponding criterion for the three-colorability of planar graphs.


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DOI: https://doi.org/10.1090/S0002-9947-1978-0515556-0
Article copyright: © Copyright 1978 American Mathematical Society