Ramsey graphs induce subgraphs of quadratically many sizes

Kwan MA, Sudakov B. 2020. Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. 2020(6), 1621–1638.


Journal Article | Published | English

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Abstract
An n-vertex graph is called C-Ramsey if it has no clique or independent set of size Clogn⁠. All known constructions of Ramsey graphs involve randomness in an essential way, and there is an ongoing line of research towards showing that in fact all Ramsey graphs must obey certain “richness” properties characteristic of random graphs. Motivated by an old problem of Erd̋s and McKay, recently Narayanan, Sahasrabudhe, and Tomon conjectured that for any fixed C, every n-vertex C-Ramsey graph induces subgraphs of Θ(n2) different sizes. In this paper we prove this conjecture.
Publishing Year
Date Published
2020-03-01
Journal Title
International Mathematics Research Notices
Volume
2020
Issue
6
Page
1621–1638
ISSN
eISSN
IST-REx-ID

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Kwan MA, Sudakov B. Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. 2020;2020(6):1621–1638. doi:10.1093/imrn/rny064
Kwan, M. A., & Sudakov, B. (2020). Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rny064
Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs of Quadratically Many Sizes.” International Mathematics Research Notices. Oxford University Press, 2020. https://doi.org/10.1093/imrn/rny064.
M. A. Kwan and B. Sudakov, “Ramsey graphs induce subgraphs of quadratically many sizes,” International Mathematics Research Notices, vol. 2020, no. 6. Oxford University Press, pp. 1621–1638, 2020.
Kwan MA, Sudakov B. 2020. Ramsey graphs induce subgraphs of quadratically many sizes. International Mathematics Research Notices. 2020(6), 1621–1638.
Kwan, Matthew Alan, and Benny Sudakov. “Ramsey Graphs Induce Subgraphs of Quadratically Many Sizes.” International Mathematics Research Notices, vol. 2020, no. 6, Oxford University Press, 2020, pp. 1621–1638, doi:10.1093/imrn/rny064.
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