An upper bound on the shortness exponent of inscribable polytopes
type: Item
instance of: scholarly article
title: An upper bound on the shortness exponent of inscribable polytopes
zbMATH Open document ID: 0676.05060
DOI: 10.1016/0095-8956(89)90008-7
author: Michael B. Dillencourt
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: The author constructs a non-Hamiltonian simplicial 3-polytope with 25 vertices inscribable into the sphere. This polytope is used as a building block for a series of examples showing that the shortness exponent of this class of polytopes is bounded from above by \(\log_ 98\). The series is constructed by the methods of \textit{B. Grünbaum} and \textit{H. Walther} [J. Comb. Theory, Ser. A 14, 364-385 (1973; Zbl 0263.05103)]. The inscribability is proved by realizing the graphs as (augmented) non- degenerate Delaunay triangulations.
reviewed by: Christoph Schulz
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 4106898
zbMATH Keywords: Hamiltonian circuit
zbMATH Keywords: 3-polytope
zbMATH Keywords: inscribable
zbMATH Keywords: shortness exponent
zbMATH Keywords: Delaunay triangulations
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90008-7
OpenAlex ID: W2064339860
cites work: Voronoi diagrams from convex hulls
cites work: Tough graphs and Hamiltonian circuits.
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cites work: Shortness exponents of families of graphs
cites work: Q5572939
cites work: Traveling salesman cycles are not always subgraphs of Voronoi duals
cites work: Simple paths on polyhedra
cites work: Connect-the-dots: A new heuristic
cites work: Q3992847
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description: scientific article; zbMATH DE number 4106898