Shortness parameters for polyhedral graphs
type: Item
instance of: scholarly article
title: Shortness parameters for polyhedral graphs
zbMATH Open document ID: 0932.05047
DOI: 10.1016/S0012-365X(98)00402-6
author: Peter J. Owens
published in: Discrete Mathematics
publication date: 2000-03-13T00:00:00Z
review text: For a family \({\mathcal F}\) of graphs the following shortness parameters are introduced: \[ \begin{aligned} \sigma ({\mathcal F}) & = \liminf_{G\in{\mathcal F}} \bigl\{\log h(G)/ \log n(G)\bigr\}, \\ \rho({\mathcal F}) & = \liminf_{G\in{\mathcal F}} \bigl\{h(G)/n(G)\},\\ \tau({\mathcal F}) & = \sup_{G\in {\mathcal F}}\bigl(n(G)-h(G)\bigr), \end{aligned} \] where \(n(G)\) is the order of \(G\) and \(h(G)\) is the circumference of \(G\). The author studies the above three parameter for various classes of polyhedral graphs. A number of known and new results are presented, and several conjectures are formulated.
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1340373
zbMATH Keywords: paths
zbMATH Keywords: cycles
zbMATH Keywords: circumference
zbMATH Keywords: polyhedral graphs
reviewed by: G. Gutin
MaRDI profile type: Publication
full work available at URL: s0012-365x(98)00402-6
OpenAlex ID: W2085204654
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description: scientific article; zbMATH DE number 1340373