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Joint extension of two theorems of Kotzig on 3-polytopes. (English) Zbl 0777.05050
By a 3-polytope is meant a planar map whose underlying graph is 3- connected. The weight of an edge is defined to be the sum of the degrees of its two ends. This paper provides that each 3-polytope has either an edge of weight at most 13 for which both incident faces are triangles, or an edge of weight at most 10 which is incident with a triangle, or else an edge of weight at most 8. All the bounds are shown to be sharp.

MSC:
 05C10 Planar graphs; geometric and topological aspects of graph theory 05C15 Coloring of graphs and hypergraphs
Keywords:
Euler formula; polytoppe; planar map; bounds
Full Text:
References:
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