A structural property of convex 3-polytopes
type: Item
instance of: scholarly article
title: A structural property of convex 3-polytopes
zbMATH Open document ID: 0893.52007
DOI: 10.1023/A:1004993723280
published in: Geometriae Dedicata
publication date: 1998-01-27T00:00:00Z
review text: A \((d_1,d_2, \dots, d_k)\)-path on a convex 3-polytope (3-connected planar graph) is one whose successive vertices have degrees \(d_1\), \(d_2, \dots, d_k\). The author shows here that a 3-polytope always has \((a,b,c)\)-paths for certain restrictions on the degrees. In particular, generalizing the (best possible) cases \(k=1\) \((a\leq 5)\) and \(k=2(a+b\leq 13\), due to \textit{A. Kotzig} [Mat.-Fyz. Čas., Slovensk. Akad. Vied 5, 101-103 (1955)]), he shows that \(a+b +c\leq 23\) is attainable; he conjectures that 21 is the correct bound.
Mathematics Subject Classification ID: 52B10
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1098493
zbMATH Keywords: 3-polytope
zbMATH Keywords: edge path
zbMATH Keywords: degree
author: Stanislav Jendroľ
reviewed by: Peter McMullen
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1098493