On face-vectors of 5-valent convex 3-polytopes
β Scribed by Stanislav Jendrol'
- Book ID
- 112499004
- Publisher
- Springer
- Year
- 1994
- Tongue
- English
- Weight
- 383 KB
- Volume
- 50
- Category
- Article
- ISSN
- 0047-2468
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The type of an edge e in a quadrangular 3-polytope is the pair of valences of the end-vertices of e. To every two valence pairs U, V the cardinal@ of the family of quadrangular 3-polytopes whose all edges have type U or V is determined.
We consider the class of simple 3-polytopes the faces of which are only triangles and 7-gons. We show that the shortness coefficient of this class is less than one. 6<q< 10.
Recently J. Zaks formulated the following Eberhard-type problem: Let (Ps, P6 .... ) be a finite sequence of nonnegative integers; does there exist a 5-valent 3-connected planar graph G such that it has exactly Pk k-gons for all k ~> 5, m i of its vertices meet exactly i triangles, 4 ~< i <~ 5, and m
It is shown that, if q >/29 and q ~ 0 (mod 3), the infinite class of 5-regular 3-polytopal graphs whose edges are incident with either two triangles or a triangle and a q-gon contains nonhamiltonian members and even has shortness exponent less than one.