Colouring of Trivalent Polyhedra
- 1 January 1965
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 17, 659-664
- https://doi.org/10.4153/cjm-1965-065-7
Abstract
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?Keywords
This publication has 2 references indexed in Scilit:
- THE EVENNESS OF THE NUMBER OF EDGES OF A CONVEX POLYHEDRONProceedings of the National Academy of Sciences, 1964
- The Number of Hexagons and the Simplicity of Geodesics on Certain PolyhedraCanadian Journal of Mathematics, 1963