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On face-vectors of 5-valent convex 3-polytopes

✍ Scribed by Stanislav Jendrol'


Book ID
112499004
Publisher
Springer
Year
1994
Tongue
English
Weight
383 KB
Volume
50
Category
Article
ISSN
0047-2468

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πŸ“œ SIMILAR VOLUMES


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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.

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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

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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.