On forwarding indices of networks
Discrete Applied Mathematics
The end structure of a graph: recent results and open problems
Discrete Mathematics - Special volume (part 1) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs”
Intersection statements for systems of sets
Journal of Combinatorial Theory Series A
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1. Noga AlonPaul Erdös [2] conjectured in 1979 that, if in a graph on n vertices any set of ⌊√n⌋ vertices contains at least one edge, then there is a set of ⌊√n⌋ vertices that contains Ω(√n log n) edges. As observed by Erdös, this result, if true, is tight. During the workshop, and after discussions with various participants including Cameron, Erdös, 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].