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Problem Collection of the DIMANET Mátraháza Workshop, 22–28 October 1995

Published online by Cambridge University Press:  01 January 1999

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Abstract

1. Noga Alon

Paul Erdős [2] conjectured in 1979 that, if in a graph on n vertices any set of [lfloor ]√n[rfloor ] vertices contains at least one edge, then there is a set of [lfloor ]√n[rfloor ] vertices that contains Ω(√n log n) edges. As observed by Erdős, this result, if true, is tight. During the workshop, and after discussions with various participants including Cameron, Erdős, Gunderson and Krivelevich, we found a proof of this conjecture, combining some probabilistic arguments with the main result of [1] (see also [3]). Hopefully this will appear in a forthcoming paper, where we also plan to include a simple proof of an extension of the main result of [1].

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 8 , Issue 1-2 , January 1999 , pp. 185 - 192
Copyright
© 1999 Cambridge University Press

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