Joint extension of two theorems of Kotzig on 3-polytopes (Q2367448)

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.