Proof of a conjecture on induced subgraphs of Ramsey graphs

Kwan MA, Sudakov B. 2019. Proof of a conjecture on induced subgraphs of Ramsey graphs. Transactions of the American Mathematical Society. 372(8), 5571–5594.


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 C log n. 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. More than 25 years ago, Erdős, Faudree and Sós conjectured that in any C-Ramsey graph there are Ω(n^5/2) induced subgraphs, no pair of which have the same numbers of vertices and edges. Improving on earlier results of Alon, Balogh, Kostochka and Samotij, in this paper we prove this conjecture.
Publishing Year
Date Published
2019-10-15
Journal Title
Transactions of the American Mathematical Society
Volume
372
Issue
8
Page
5571-5594
ISSN
eISSN
IST-REx-ID

Cite this

Kwan MA, Sudakov B. Proof of a conjecture on induced subgraphs of Ramsey graphs. Transactions of the American Mathematical Society. 2019;372(8):5571-5594. doi:10.1090/tran/7729
Kwan, M. A., & Sudakov, B. (2019). Proof of a conjecture on induced subgraphs of Ramsey graphs. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/7729
Kwan, Matthew Alan, and Benny Sudakov. “Proof of a Conjecture on Induced Subgraphs of Ramsey Graphs.” Transactions of the American Mathematical Society. American Mathematical Society, 2019. https://doi.org/10.1090/tran/7729.
M. A. Kwan and B. Sudakov, “Proof of a conjecture on induced subgraphs of Ramsey graphs,” Transactions of the American Mathematical Society, vol. 372, no. 8. American Mathematical Society, pp. 5571–5594, 2019.
Kwan MA, Sudakov B. 2019. Proof of a conjecture on induced subgraphs of Ramsey graphs. Transactions of the American Mathematical Society. 372(8), 5571–5594.
Kwan, Matthew Alan, and Benny Sudakov. “Proof of a Conjecture on Induced Subgraphs of Ramsey Graphs.” Transactions of the American Mathematical Society, vol. 372, no. 8, American Mathematical Society, 2019, pp. 5571–94, doi:10.1090/tran/7729.
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