Goddard, Wayne; Henning, Michael A.; Oellermann, Ortrud R. Bipartite Ramsey numbers and Zarankiewicz numbers. (English) Zbl 0953.05051 Discrete Math. 219, No. 1-3, 85-95 (2000). Authors’ abstract: The Zarankiewicz number \(z(s,m)\) is the maximum number of edges in a subgraph of \(K(s,s)\) that does not contain \(K(m,m)\) as a subgraph. The bipartite Ramsey number \(b(m,n)\) is the least positive integer \(b\) such that if the edges of \(K(b,b)\) are coloured with red and blue, then there always exists a blue \(K(m,m)\) or a read \(K(n,n)\). In this paper we calculate small exact values of \(z(s,2)\) and determine bounds for Zarankiewicz numbers in general. The latter are used to bound \(b(m,n)\) for \(m,n\leq 6\). Reviewer: Jack E.Graver (Syracuse) Cited in 10 Documents MSC: 05C55 Generalized Ramsey theory 05C35 Extremal problems in graph theory Keywords:Zarankiewicz number; bipartite Ramsey number; bound PDFBibTeX XMLCite \textit{W. Goddard} et al., Discrete Math. 219, No. 1--3, 85--95 (2000; Zbl 0953.05051) Full Text: DOI Online Encyclopedia of Integer Sequences: Maximum number of edges in a squarefree bipartite graph on n vertices.