TkSE, M., Shortness coefficients of simple 3-polytopal graphs with edges of only two types, Discrete Mathematics 103 (1992) 103-110. We consider two classes of simple 3-polytopal graphs whose edges are incident with either two S-gons or a 5-gon and q-gon (q = 26 or 27). We show that the shortness c
On shortness coefficients of simple 3-polytopal graphs with only one type of faces besides triangles
✍ Scribed by Michal Tkáč
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 328 KB
- Volume
- 128
- Category
- Article
- ISSN
- 0012-365X
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✦ Synopsis
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.
📜 SIMILAR VOLUMES
We consider classes of simple 3-polytopal graphs whose edges are incident with either two 5-gons or a 5-gon and a q-gon (q > 5). We show that the shortness coefficient is less than one for all q 1> 28, settle a question raised by Jendrol and Tk~i~ in a recent paper in this journal and prove that all
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.
We consider the class of pentagonal 3-polytopal graphs all of whose edges are incident either with two 3-valent vertices or with a 3-valent vertex and a q-valent vertex. For most values of q, (i) we find a small non-hamiltonian graph in the class and (ii) we show that the shortness exponent of the c
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