{"publication_status":"published","scopus_import":"1","article_type":"original","type":"journal_article","oa_version":"Preprint","page":"619-630","volume":53,"main_file_link":[{"url":"https://arxiv.org/abs/1912.07722","open_access":"1"}],"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"publisher":"Wiley","issue":"2","publication":"Bulletin of the London Mathematical Society","date_created":"2021-06-21T06:11:56Z","citation":{"apa":"Fox, J., Kwan, M. A., &#38; Sudakov, B. (2021). Acyclic subgraphs of tournaments with high chromatic number. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12446\">https://doi.org/10.1112/blms.12446</a>","chicago":"Fox, Jacob, Matthew Alan Kwan, and Benny Sudakov. “Acyclic Subgraphs of Tournaments with High Chromatic Number.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2021. <a href=\"https://doi.org/10.1112/blms.12446\">https://doi.org/10.1112/blms.12446</a>.","ama":"Fox J, Kwan MA, Sudakov B. Acyclic subgraphs of tournaments with high chromatic number. <i>Bulletin of the London Mathematical Society</i>. 2021;53(2):619-630. doi:<a href=\"https://doi.org/10.1112/blms.12446\">10.1112/blms.12446</a>","ieee":"J. Fox, M. A. Kwan, and B. Sudakov, “Acyclic subgraphs of tournaments with high chromatic number,” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2. Wiley, pp. 619–630, 2021.","ista":"Fox J, Kwan MA, Sudakov B. 2021. Acyclic subgraphs of tournaments with high chromatic number. Bulletin of the London Mathematical Society. 53(2), 619–630.","mla":"Fox, Jacob, et al. “Acyclic Subgraphs of Tournaments with High Chromatic Number.” <i>Bulletin of the London Mathematical Society</i>, vol. 53, no. 2, Wiley, 2021, pp. 619–30, doi:<a href=\"https://doi.org/10.1112/blms.12446\">10.1112/blms.12446</a>.","short":"J. Fox, M.A. Kwan, B. Sudakov, Bulletin of the London Mathematical Society 53 (2021) 619–630."},"doi":"10.1112/blms.12446","abstract":[{"lang":"eng","text":"We prove that every n-vertex tournament G has an acyclic subgraph with chromatic number at least n5/9−o(1), while there exists an n-vertex tournament G whose every acyclic subgraph has chromatic number at most n3/4+o(1). This establishes in a strong form a conjecture of Nassar and Yuster and improves on another result of theirs. Our proof combines probabilistic and spectral techniques together with some additional ideas. In particular, we prove a lemma showing that every tournament with many transitive subtournaments has a large subtournament that is almost transitive. This may be of independent interest."}],"year":"2021","day":"03","article_processing_charge":"No","oa":1,"date_published":"2021-04-03T00:00:00Z","_id":"9572","author":[{"first_name":"Jacob","full_name":"Fox, Jacob","last_name":"Fox"},{"full_name":"Kwan, Matthew Alan","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","orcid":"0000-0002-4003-7567","first_name":"Matthew Alan"},{"first_name":"Benny","full_name":"Sudakov, Benny","last_name":"Sudakov"}],"title":"Acyclic subgraphs of tournaments with high chromatic number","status":"public","extern":"1","intvolume":"        53","month":"04","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","external_id":{"arxiv":["1912.07722"]},"quality_controlled":"1","date_updated":"2023-02-23T14:01:21Z","language":[{"iso":"eng"}]}