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Bipartite Ramsey numbers and Zarankiewicz numbers

13 years 11 months ago
Bipartite Ramsey numbers and Zarankiewicz numbers
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 red 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 6. Key words: Graphs, bipartite Ramsey numbers, Zarankiewicz, bicliques
Wayne Goddard, Michael A. Henning, Ortrud R. Oelle
Added 18 Dec 2010
Updated 18 Dec 2010
Type Journal
Year 2000
Where DM
Authors Wayne Goddard, Michael A. Henning, Ortrud R. Oellermann
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