On the crossing number of \(K_{m,n}\)
type: Item
instance of: scholarly article
title: On the crossing number of \(K_{m,n}\)
zbMATH Open document ID: 1023.05039
author: Nagi H. Nahas
published in: The Electronic Journal of Combinatorics
publication date: 2003-09-24T00:00:00Z
full work available at URL: v10i1n8.html
review text: Summary: The best lower bound known on the crossing number of the complete bipartite graph is \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2\rfloor\lfloor(n-1)/2\rfloor.\) We prove that \(\text{cr}(K_{m,n}) \geq (1/5)m(m-1)\lfloor n/2 \rfloor \lfloor (n-1)/2 \rfloor + 9.9 \times 10^{-6} m^2n^2\) for sufficiently large \(m\) and \(n\).
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1985383
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1985383