The smallest non-Hamiltonian 3-connected cubic planar graphs have 38 vertices
type: Item
instance of: scholarly article
title: The smallest non-Hamiltonian 3-connected cubic planar graphs have 38 vertices
zbMATH Open document ID: 0607.05051
DOI: 10.1016/0095-8956(88)90075-5
published in: Journal of Combinatorial Theory. Series B
publication date: 1988-01-01T00:00:00Z
review text: We show that all 3-connected cubic planar graphs on 36 or fewer vertices are hamiltonian, thus extending results of Lederberg, Butler, Goodey, Wegner, Okamura and Barnette. Furthermore, the only non-hamiltonian examples on 38 vertices which are not cyclically 4-connected are the six graphs which have been found by Lederberg, Barnette and Bosák.
Mathematics Subject Classification ID: 05C45
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 52Bxx
zbMATH DE Number: 3981218
zbMATH Keywords: cubic planar graphs
zbMATH Keywords: convex polytope
zbMATH Keywords: simplex polytope
zbMATH Keywords: Hamiltonian cycle
zbMATH Keywords: non-Hamiltonian graph
Wikidata QID: Q55933544
author: Derek Holton
author: Brendan D. McKay
describes a project that uses: nauty
MaRDI profile type: Publication
full work available at URL: 0095-8956(88)90075-5
OpenAlex ID: W2051837347
cites work: Every simple 3-polytype with 34 vertices is Hamiltonian
cites work: Hamiltonian circuits in simple 3-polytopes with up to 26 vertices
cites work: Q5575344
cites work: Hamiltonian circuits on simple 3-polytopes
cites work: Q4096968
cites work: Non-Hamiltonian cubic planar maps
cites work: Hamiltonian Circuits on Simple 3-Polytopes
cites work: Q5547252
cites work: Polytopes, graphs, and complexes
cites work: Hamilton Circuits of Convex Trivalent Polyhedra (Up to 18 Vertices)
cites work: Q3313897
cites work: Hamiltonian circuits on simple 3-polytopes with up to 30 vertices
cites work: Every simple 3-polytope of order 32 or less is Hamiltonian
DBLP publication ID: journals/jct/HoltonM88
description: scientific article; zbMATH DE number 3981218