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Ramsey games with giants

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posted on 01.03.2010, 00:00 by Tom Bohman, Alan FriezeAlan Frieze, Michael Krivelevich, Po-Shen Loh, Benny Sudakov

The classical result in the theory of random graphs, proved by Erd˝os and R´enyi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in a sequence of rounds must be colored with one of r colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.

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Publisher Statement

This is the accepted version of the article which has been published in final form at http://dx.doi.org/10.1002/rsa.20343

Date

01/03/2010

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