Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane
type: Item
instance of: scholarly article
title: Generating the 4-connected and strongly 4-connected triangulations on the torus and projective plane
zbMATH Open document ID: 0728.05018
DOI: 10.1016/0012-365X(90)90159-F
author: D. W. Barnette
published in: Discrete Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The triangulations of the projective plane were shown by the author to be generated by the operation of vertex splitting from two minimal triangulations [``Generating the triangulations of the projective plane'', J. Comb. Theory, Ser. B 33, 222-230 (1982; Zbl 0509.52007)]. He shows here that if the same operation is applied to the same starting set of triangulations, but restricted so that vertices of degree 3 are never created, then the set of 4-connected triangulations of the projective plane is generated. With the additional restriction that two adjacent vertices of degree 4 are never created, the set of strongly 4-connected triangulations results. (A graph is strongly 4-connected if it is 4- connected and the removal of any 4-vertex-cut leaves a component which is a vertex.) The analogous statements are shown to be valid for the torus, with a starting set of 21 minimal triangulations.
reviewed by: Nicholas Wormald
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 51E15
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 4202275
zbMATH Keywords: triangulations
zbMATH Keywords: projective plane
MaRDI profile type: Publication
cites work: On generating planar graphs
cites work: Generating planar 4-connected graphs
cites work: Generating the triangulations of the projective plane
cites work: Graph theorems for manifolds
cites work: Q5589866
cites work: Q3766517
cites work: Q5597451
cites work: Q4089424
full work available at URL: 0012-365x(90)90159-f
OpenAlex ID: W2069178656
description: scientific article; zbMATH DE number 4202275