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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
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.

References [Enhancements On Off] (What's this?)

  • [1] E. Akin, Manifold phenomena in the theory ofpolyhedra, Trans. Amer. Math. Soc. 143 (1969), 413-473. MR 0253329 (40:6544)
  • [2] K. Appel and W. Haken, Every planar map is four colorable, Bull. Amer. Math. Soc. 82 (1976), 711-712; Illinois J. Math. 21 (1977), 429-567. MR 0424602 (54:12561)
  • [3] N. C. Dalkey, Parity patterns on even triangulated polygons, J. Combinatorial Theory 2 (1967), 100-103. MR 0204315 (34:4159)
  • [4] O. Ore, The four color problem, Academic Press, New York, 1967. MR 0216979 (36:74)

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Article copyright: © Copyright 1978 American Mathematical Society

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