Simple 3-polytopal graphs with edges of only two types and shortness coefficients
type: Item
instance of: scholarly article
title: Simple 3-polytopal graphs with edges of only two types and shortness coefficients
zbMATH Open document ID: 0586.05027
DOI: 10.1016/0012-365X(86)90074-9
published in: Discrete Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Simple planar 3-connected trivalent graphs are considered with only two types of faces: 5-gons and q-gons, in which no two q-gons have a common edge. For any \(q\geq 28\) infinitely many non-Hamltonian graphs are constructed. It also follows that for large enough q values any cycle in these graphs misses at least 1/60 of the vertices, thereby radically improving previous results. For all \(q\geq 16\) infinite families of graphs (not necessarily non-Hamiltonian) are constructed. It is also shown that that any graph with \(q\geq 6\) is cyclically 4-edge connected.
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 51M20
Mathematics Subject Classification ID: 05C45
zbMATH DE Number: 3939393
zbMATH Keywords: planar 3-connected graphs
zbMATH Keywords: shortness coefficient
zbMATH Keywords: non-Hamltonian graphs
zbMATH Keywords: cyclically 4-edge connected
author: Peter J. Owens
reviewed by: Frank Plastria
MaRDI profile type: Publication
cites work: Non-Hamiltonian cubic planar maps
cites work: Pairs of edge-disjoint Hamiltonian circuits
cites work: Shortness exponents of families of graphs
cites work: On the simplicial 3-polytopes with only two types of edges
cites work: Shortness parameters of families of regular planar graphs in two or three types of faces
cites work: Cyclically 5-edge-connected cubic planar graphs and shortness coefficients
cites work: Regular planar graphs with faces of only two types and shortness parameters
cites work: Shortness parameters for planar graphs with faces of only one type
cites work: Note on two problems of J. Zaks concerning Hamiltonian 3-polytopes
cites work: Non-Hamiltonian simple 3-polytopes having just two types of faces
full work available at URL: 0012-365x(86)90074-9
OpenAlex ID: W2035239952
description: scientific article; zbMATH DE number 3939393