Sphericity exceeds cubicity for almost all complete bipartite graphs
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.
scientific article; zbMATH DE number 3957139