On the shortness exponent of 1-tough, maximal planar graphs
type: Item
instance of: scholarly article
title: On the shortness exponent of 1-tough, maximal planar graphs
zbMATH Open document ID: 0852.05055
DOI: 10.1016/0012-365X(94)00356-N
author: Michal Tkáč
published in: Discrete Mathematics
publication date: 1996-11-25T00:00:00Z
review text: The notion of shortness exponent of a family of graphs was introduced by \textit{B. Grünbaum} and \textit{H. Walther} [J. Comb. Theory, Ser. A 14, 364-385 (1973; Zbl 0263.05103)]. A graph \(G\) is said to be 1-tough if for any non-empty set \(S\) of vertices of \(G\), the number of components of \(G-S\) is smaller than the number of vertices in \(S\), see \textit{V. Chvátal} [Tough graphs and Hamiltonian circuits, Discrete Math. 5, 215-228 (1973; Zbl 0256.05122)]. In the paper of the author, a bound for the shortness exponent of a class of 1-tough planar graphs is presented.
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 906918
zbMATH Keywords: shortness exponent
zbMATH Keywords: planar graphs
reviewed by: Ernest Jucovič
MaRDI profile type: Publication
cites work: Hamiltonian circuits on 3-polytopes
cites work: Tough graphs and Hamiltonian circuits.
cites work: An upper bound on the shortness exponent of 1-tough, maximal planar graphs
cites work: Q5547252
cites work: Shortness exponents of families of graphs
cites work: Toughness and nonhamiltonicity of polyhedral graphs
cites work: Non-hamiltonian \(5 \over 4\)-tough maximal planar graphs
cites work: The smallest non-Hamiltonian 3-connected cubic planar graphs have 38 vertices
cites work: Q3921768
cites work: A 1-tough nonhamiltonian maximal planar graph
description: scientific article; zbMATH DE number 906918