Generating closed 2-cell embeddings in the torus and the projective plane
type: Item
instance of: scholarly article
title: Generating closed 2-cell embeddings in the torus and the projective plane
zbMATH Open document ID: 0614.51008
DOI: 10.1007/BF02187881
author: D. W. Barnette
published in: Discrete \& Computational Geometry
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/131020
review text: If a graph is embedded in a 2-manifold such that all faces are cells bounded by simple closed curves, it is called a closed 2-cell embedding of the graph in the manifold. Among the various results for the recursive generation of 2-cell complexes and their graphs the Steinitz-theorem on planar 3-connected graphs is by far the best known. The author proves that the 2-cell embeddings in the projective plane can be generated from two minimal graphs, and in the case of the torus from six minimal graphs by vertex splitting and face splitting.
Mathematics Subject Classification ID: 51H20
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 57M20
Mathematics Subject Classification ID: 57M15
zbMATH DE Number: 3994416
zbMATH Keywords: 2-cell embeddings in the projective plane
zbMATH Keywords: torus
zbMATH Keywords: minimal graphs
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
cites work: On generating planar graphs
cites work: Generating planar 4-connected graphs
cites work: A Generation Procedure for the Simple 3-Polytopes With Cyclically 5-Connected Graphs
cites work: Q4089424
cites work: Q3284374
OpenAlex ID: W1991392666
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description: scientific article; zbMATH DE number 3994416