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Joint extension of two theorems of Kotzig on 3-polytopes

✍ Scribed by Oleg Borodin

Publisher
Springer-Verlag
Year
1993
Tongue
English
Weight
233 KB
Volume
13
Category
Article
ISSN
0209-9683

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πŸ“œ SIMILAR VOLUMES

On the simplicial 3-polytopes with only
On the simplicial 3-polytopes with only two types of edges
✍ Stanislav JendroΔΎ; Michal TkÑč πŸ“‚ Article πŸ“… 1984 πŸ› Elsevier Science 🌐 English βš– 492 KB

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

Note on two problems of J. Zaks concerni
Note on two problems of J. Zaks concerning Hamiltonian 3-polytopes
✍ Hansjoachim Walther πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 313 KB

Let us denote by G(m, n) the family of all simple 3-poiytopes having ,just two types of faces, m-gons and n-gons. J. Z&s [3] proved that G(5; k) contains non-Hamiltonian members for all k, k 3 11, and asked among others the folfowing question: Do there exist non-Hamiltonian members in any of the fam

On quadrangular convex 3-polytopes with
On quadrangular convex 3-polytopes with at most two types of edges
✍ Stanislav JendrolΛ‡; Ernest Jucovič πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 681 KB

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.

5-regular 3-polytopal graphs with edges
5-regular 3-polytopal graphs with edges of only two types and shortness exponents less than one
✍ J. Harant; P.J. Owens; M. TkÑč; H. Walther πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 309 KB

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.