The final size of the c4-free process

Authors:
Michael e. Picollelli
Affiliations:
Department of electrical and computer engineering, university of delaware, newark, de, usa (e-mail: mpicolle@udel.edu)
Venue:
Combinatorics, Probability and Computing
Year:
2011

Citing 6
Cited 0

Counting extensions

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Coloring graphs with sparse neighborhoods

Journal of Combinatorial Theory Series B
Random maximal H-free graphs

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On the size of a random maximal graph

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The Ramsey number R(3, t) has order of magnitude t2/log t

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Triangle-free subgraphs in the triangle-free process

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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 â聠聮 ∞, 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.