Sphericity exceeds cubicity for almost all complete bipartite graphs
type: Item
instance of: scholarly article
title: Sphericity exceeds cubicity for almost all complete bipartite graphs
zbMATH Open document ID: 0595.05031
DOI: 10.1016/0095-8956(86)90081-X
author: H. Maehara
published in: Journal of Combinatorial Theory. Series B
publication date: 1986-01-01T00:00:00Z
review text: The sphericity of a graph \(G\) is the smallest integer \(n\) such that the nodes of \(G\) can be embedded in \(E^ n\) in such a way that the Euclidean distance of a pair of nodes is smaller than 1 if and only if the nodes are adjacent in \(G\). The cubicity of \(G\) is defined similarly where the distance is replaced by the subnorm. The author proves that for complete bipartite graphs \(K(m,n)\) with \(\max (m,n)\geq n_ 0\) the sphericity exceeds the cubicity.
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 3957139
zbMATH Keywords: sphericity
zbMATH Keywords: cubicity
zbMATH Keywords: complete bipartite graphs
reviewed by: Peter Kleinschmidt
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3957139