Projective plane embeddings of polyhedral pinched maps
type: Item
instance of: scholarly article
title: Projective plane embeddings of polyhedral pinched maps
zbMATH Open document ID: 0794.05022
DOI: 10.1016/0012-365X(94)90272-0
author: Adrian Riskin
published in: Discrete Mathematics
publication date: 1994-04-04T00:00:00Z
review text: A map (or embedding of a graph in a compact 2-manifold) is called closed 2-cell provided that the closure of each region is a 2-cell. A polyhedral map on the pinched torus is called a pinched polyhedral map, and the projective plane is denoted by \(\Pi\). The first part deals with two cases in which a pinched polyhedral map is not \(\Pi\)-embeddable. The main result states that a \(\Pi\)-embedding of a pinched polyhedral map must be closed 2-cell, but cannot be polyhedral.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 57M20
zbMATH DE Number: 540944
zbMATH Keywords: map
zbMATH Keywords: embedding
zbMATH Keywords: closed 2-cell
zbMATH Keywords: pinched polyhedral map
zbMATH Keywords: projective plane
reviewed by: Stelian Mihalas
MaRDI profile type: Publication
cites work: On the noninterpolation of polyhedral maps
cites work: Graph theorems for manifolds
cites work: Polyhedral embeddings in the projective plane
cites work: Q3818315
cites work: Embeddings of graphs with no short noncontractible cycles
cites work: Q4273853
full work available at URL: 0012-365x(94)90272-0
OpenAlex ID: W2066343349
description: scientific article; zbMATH DE number 540944