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Colouring of Trivalent Polyhedra

Published online by Cambridge University Press:  20 November 2018

Anton Kotzig
Anton Kotzig*
Affiliation:
Komensky University, Bratislava, Czechoslovakia
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By an Euler polyhedron of valence three or a trivalent convex polyhedron in Euclidean 3-space (4) we mean in the present paper an Euler polyhedron in the sense of Steinitz (8, p. 113), such that each vertex is incident with exactly three edges.

In the present paper we establish a theorem concerning the colouring of trivalent polyhedra. A specialization of this theorem solves the following problem implicit in Eberhard (1, p. 84): Does there exist a trivalent Euler polyhedron with an odd number of faces such that the number of edges incident with any face is divisible by three?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 659 - 664
Copyright
Copyright © Canadian Mathematical Society 1965

References

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