The orientable genus of some joins of complete graphs with large edgeless graphs
type: Item
instance of: scholarly article
title: The orientable genus of some joins of complete graphs with large edgeless graphs
zbMATH Open document ID: 1182.05042
author: D. Christopher Stephens
author: M. N. Ellingham
published in: Discrete Mathematics
publication date: 2009-04-09T00:00:00Z
review text: The authors investigate the orientable genus of the join of a complete graph \(K_n\) with a large edgeless graph \(\overline{K_m}\). Concretely, they show that the genus of \(\overline{K_m}+K_n\) is equal to that of the complete bipartite graph \(K_{m,n}\) if \(n\) is even and \(m \geq n\). Also it is shown that the quality holds when \(n=2^p+2, p\geq 3\) and \(m\geq n-1\), or when \(n=2^p+1, p\geq 3\) and \(m\geq n+1\).
reviewed by: Youngsik Huh
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5542437
zbMATH Keywords: orientable genus
zbMATH Keywords: bipartite graph
zbMATH Keywords: complete graph
MaRDI profile type: Publication
full work available at URL: j.disc.2007.12.098
OpenAlex ID: W2147224583
cites work: Orientable and non orientable genus of the complete bipartite graph
cites work: On the genus of joins and compositions of graphs
cites work: The nonorientable genus of joins of complete graphs with large edgeless graphs
cites work: Counterexamples to the nonorientable genus conjecture for complete tripartite graphs
cites work: The nonorientable genus of complete tripartite graphs
cites work: Hamiltonian embeddings from triangulations
cites work: Q3757929
cites work: Orientable triangular embeddings of K\(_{18}\)-K\(_3\) and K\(_{13}\)-K\(_3\)
cites work: Orientable and Nonorientable Genera for Some Complete Tripartite Graphs
cites work: Triangular embeddings of \(K_n-K_m\) with unboundedly large \(m\)
cites work: Minimal ordered triangulations of surfaces
cites work: Q3712350
cites work: Graphs on surfaces
cites work: Der vollständige paare Graph auf nichtorientierbaren Flächen.
cites work: Das Geschlecht des vollständigen paaren Graphen
cites work: Q4773723
cites work: Das Geschlecht des vollständigen dreifärbbaren Graphen
DOI: 10.1016/J.DISC.2007.12.098
description: scientific article; zbMATH DE number 5542437