On smallest \(3\)-polytopes of given graph radius

The \(3\)-polytopes are planar, \(3\)-connected graphs. A classical question is, for \(r\geq 3\), is the \(2(r-1)\)-gonal prism \(K_2\times C_{2(r-1)}\) the unique \(3\)-polytope of graph radius \(r\) and smallest size? Under some extra assumptions, we answer this question in the positive.

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Bibliographic Details
Published inarXiv.org
Main Authors Maffucci, Riccardo W, Willems, Niels
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.07.2022
Subjects
Polytopes
Questions
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Summary:The \(3\)-polytopes are planar, \(3\)-connected graphs. A classical question is, for \(r\geq 3\), is the \(2(r-1)\)-gonal prism \(K_2\times C_{2(r-1)}\) the unique \(3\)-polytope of graph radius \(r\) and smallest size? Under some extra assumptions, we answer this question in the positive.
ISSN:2331-8422