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The Final Size of the C4-Free Process

Published online by Cambridge University Press:  05 September 2011

MICHAEL E. PICOLLELLI
MICHAEL E. PICOLLELLI*
Affiliation:
Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA (e-mail: [email protected])
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Abstract

We consider the following random graph process: starting with n isolated vertices, add edges uniformly at random provided no such edge creates a copy of C4. We show that, with probability tending to 1 as n → ∞, the final graph produced by this process has maximum degree O((nlogn)1/3) and consequently size O(n4/3(logn)1/3), which are sharp up to constants. This confirms conjectures of Bohman and Keevash and of Osthus and Taraz, and improves upon previous bounds due to Bollobás and Riordan and Osthus and Taraz.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 6 , November 2011 , pp. 939 - 955
Copyright
Copyright © Cambridge University Press 2011

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