A cyclic coloration of a planar graph G is an assignment of colors to the points of G such that for any face bounding cycle the points of f have different colors. We observe that the upper bound 2p\*(G), due to 0. Ore and M. D. Plummer, can be improved to p \* ( G ) + 9 when G is 3connected (p\* den
Incidence-polytopes of type {6, 3, 3}
✍ Scribed by Asia Ivić Weiss
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 367 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0046-5755
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📜 SIMILAR VOLUMES
We consider convex 3-polytopes with exactly two types of edges. The questions of the existence of such 3-polytopes are solved. The cardinalities of all classes are determined.
A. Kotzig [5] proved the following theorem (cf. B. Griinbaum [2,3,4]: Every 3-polytope has at least one edge such that the sum of valencies of its end-vertices is ~< 13. In this note we deal with improvements of this statement. Let us review first some of the notations employed: If we are given a p
For some families of graphs of simplicial 3-polytopes with two types of edges structural properties are described, for other ones their cardinality is determined. ## 1. ln~oduction Griinbaum and Motzkin [3], Griinbaum and Zaks [4], and Malkevitch [6] investigated the structural properties of triva