Cantankerous maps and rotary embeddings of \(K_ n\)
type: Item
instance of: scholarly article
title: Cantankerous maps and rotary embeddings of \(K_ n\)
zbMATH Open document ID: 0687.05018
DOI: 10.1016/0095-8956(89)90028-2
published in: Journal of Combinatorial Theory. Series B
publication date: 1989-01-01T00:00:00Z
review text: A regular map is a 2-cell embedding of some graph on a closed surface such that the automorphism group of the embedding acts transitively on the flags, i.e., the triples consisting of a vertex, edge and face that are mutually incident. The author studies a class of non-orientable regular maps that contain an orientation-reversing cycle of length 2 and calls them cantankerous. He establishes various properties of cantankerous maps and shows that every regular map whose underlying graph is not simple is either cantankerous or is an appropriate branched covering over a regular map of a simple graph. Finally he applies the results to show that the complete graph of order greater than 6 (possibly with multiple edges of the same multiplicity) has no regular map. The same result (with multiplicity one) was established by \textit{L. D. James} [Ars Comb. 16-B, 57-72 (1983; Zbl 0539.05029)].
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 4125421
zbMATH Keywords: vertex-proper rotary map
zbMATH Keywords: regular map
zbMATH Keywords: cantankerous maps
zbMATH Keywords: multiplicity
author: Steve Wilson
MaRDI profile type: Publication
full work available at URL: 0095-8956(89)90028-2
OpenAlex ID: W2038736879
cites work: Automorphisms of imbedded graphs
cites work: Q5654065
cites work: Q4049712
cites work: Q3273607
cites work: Q5650865
cites work: Regular orientable imbeddings of complete graphs
cites work: Operators over regular maps
cites work: Riemann Surfaces Over Regular Maps
description: scientific article; zbMATH DE number 4125421