{"date_published":"2019-10-15T00:00:00Z","external_id":{"arxiv":["1712.05656"]},"date_created":"2021-06-22T09:31:45Z","abstract":[{"text":"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.","lang":"eng"}],"doi":"10.1090/tran/7729","year":"2019","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","issue":"8","month":"10","day":"15","publication":"Transactions of the American Mathematical Society","oa_version":"Submitted Version","publisher":"American Mathematical Society","quality_controlled":"1","language":[{"iso":"eng"}],"title":"Proof of a conjecture on induced subgraphs of Ramsey graphs","article_type":"original","author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567"},{"first_name":"Benny","last_name":"Sudakov","full_name":"Sudakov, Benny"}],"article_processing_charge":"No","publication_status":"published","extern":"1","status":"public","main_file_link":[{"url":"https://doi.org/10.1090/tran/7729","open_access":"1"}],"page":"5571-5594","intvolume":"       372","volume":372,"oa":1,"_id":"9585","publication_identifier":{"eissn":["1088-6850"],"issn":["0002-9947"]},"citation":{"chicago":"Kwan, Matthew Alan, and Benny Sudakov. “Proof of a Conjecture on Induced Subgraphs of Ramsey Graphs.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2019. <a href=\"https://doi.org/10.1090/tran/7729\">https://doi.org/10.1090/tran/7729</a>.","ama":"Kwan MA, Sudakov B. Proof of a conjecture on induced subgraphs of Ramsey graphs. <i>Transactions of the American Mathematical Society</i>. 2019;372(8):5571-5594. doi:<a href=\"https://doi.org/10.1090/tran/7729\">10.1090/tran/7729</a>","apa":"Kwan, M. A., &#38; Sudakov, B. (2019). Proof of a conjecture on induced subgraphs of Ramsey graphs. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/7729\">https://doi.org/10.1090/tran/7729</a>","ieee":"M. A. Kwan and B. Sudakov, “Proof of a conjecture on induced subgraphs of Ramsey graphs,” <i>Transactions of the American Mathematical Society</i>, vol. 372, no. 8. American Mathematical Society, pp. 5571–5594, 2019.","ista":"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.","short":"M.A. Kwan, B. Sudakov, Transactions of the American Mathematical Society 372 (2019) 5571–5594.","mla":"Kwan, Matthew Alan, and Benny Sudakov. “Proof of a Conjecture on Induced Subgraphs of Ramsey Graphs.” <i>Transactions of the American Mathematical Society</i>, vol. 372, no. 8, American Mathematical Society, 2019, pp. 5571–94, doi:<a href=\"https://doi.org/10.1090/tran/7729\">10.1090/tran/7729</a>."},"scopus_import":"1","date_updated":"2023-02-23T14:01:50Z","type":"journal_article"}