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A Sequence of Triangle-Free Pseudorandom Graphs

Published online by Cambridge University Press:  13 September 2016

DAVID CONLON*
Affiliation:
Mathematical Institute, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, UK (e-mail: [email protected])

Abstract

A construction of Alon yields a sequence of highly pseudorandom triangle-free graphs with edge density significantly higher than one might expect from comparison with random graphs. We give an alternative construction for such graphs.

Type
Paper
Copyright
Copyright © Cambridge University Press 2016 

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References

[1] Alon, N. (1994) Explicit Ramsey graphs and orthonormal labelings. Electron. J. Combin. 1 R12.Google Scholar
[2] Alon, N. and Kahale, N. (1998) Approximating the independence number via the θ-function. Math. Program. 80 253264.Google Scholar
[3] Bohman, T. (2009) The triangle-free process. Adv. Math. 221 16531677.Google Scholar
[4] Conlon, D., Fox, J. and Zhao, Y. (2014) Extremal results in sparse pseudorandom graphs. Adv. Math. 256 206290.Google Scholar
[5] Erdős, P., Goldberg, M., Pach, J. and Spencer, J. (1988) Cutting a graph into two dissimilar halves. J. Graph Theory 12 121131.CrossRefGoogle Scholar
[6] Erdős, P. and Spencer, J. (1971/72) Imbalances in k-colorations. Networks 1 379385.Google Scholar
[7] Hanson, D. L. and Wright, F. T. (1971) A bound on tail probabilities for quadratic forms in independent random variables. Ann. Math. Statist. 42 10791083.CrossRefGoogle Scholar
[8] Krivelevich, M. and Sudakov, B. (2006) Pseudo-random graphs. In More Sets, Graphs and Numbers, Vol. 15 of Bolyai Society Mathematical Studies, Springer, pp. 199262.Google Scholar
[9] Lazebnik, F., Ustimenko, V. A. and Woldar, A. J. (1999) Polarities and 2k-cycle-free graphs. Discrete Math. 197/198 503513.Google Scholar
[10] Rudelson, M. and Vershynin, R. (2013) Hanson–Wright inequality and sub-Gaussian concentration. Electron. Commun. Probab. 18 19.Google Scholar