{"publisher":"Springer","external_id":{"arxiv":["1810.12144"]},"month":"04","date_created":"2021-06-22T06:42:26Z","publication_status":"published","issue":"2","publication":"Combinatorica","oa_version":"Preprint","doi":"10.1007/s00493-019-4086-0","date_updated":"2023-02-23T14:01:45Z","type":"journal_article","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","_id":"9582","extern":"1","status":"public","article_type":"original","oa":1,"abstract":[{"text":"The problem of finding dense induced bipartite subgraphs in H-free graphs has a long history, and was posed 30 years ago by Erdős, Faudree, Pach and Spencer. In this paper, we obtain several results in this direction. First we prove that any H-free graph with minimum degree at least d contains an induced bipartite subgraph of minimum degree at least cH log d/log log d, thus nearly confirming one and proving another conjecture of Esperet, Kang and Thomassé. Complementing this result, we further obtain optimal bounds for this problem in the case of dense triangle-free graphs, and we also answer a question of Erdœs, Janson, Łuczak and Spencer.","lang":"eng"}],"year":"2020","page":"283-305","main_file_link":[{"url":"https://arxiv.org/abs/1810.12144","open_access":"1"}],"author":[{"id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","first_name":"Matthew Alan"},{"full_name":"Letzter, Shoham","first_name":"Shoham","last_name":"Letzter"},{"first_name":"Benny","last_name":"Sudakov","full_name":"Sudakov, Benny"},{"first_name":"Tuan","last_name":"Tran","full_name":"Tran, Tuan"}],"day":"01","language":[{"iso":"eng"}],"title":"Dense induced bipartite subgraphs in triangle-free graphs","intvolume":"        40","citation":{"ieee":"M. A. Kwan, S. Letzter, B. Sudakov, and T. Tran, “Dense induced bipartite subgraphs in triangle-free graphs,” <i>Combinatorica</i>, vol. 40, no. 2. Springer, pp. 283–305, 2020.","apa":"Kwan, M. A., Letzter, S., Sudakov, B., &#38; Tran, T. (2020). Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. Springer. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>","ama":"Kwan MA, Letzter S, Sudakov B, Tran T. Dense induced bipartite subgraphs in triangle-free graphs. <i>Combinatorica</i>. 2020;40(2):283-305. doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>","chicago":"Kwan, Matthew Alan, Shoham Letzter, Benny Sudakov, and Tuan Tran. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00493-019-4086-0\">https://doi.org/10.1007/s00493-019-4086-0</a>.","short":"M.A. Kwan, S. Letzter, B. Sudakov, T. Tran, Combinatorica 40 (2020) 283–305.","mla":"Kwan, Matthew Alan, et al. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” <i>Combinatorica</i>, vol. 40, no. 2, Springer, 2020, pp. 283–305, doi:<a href=\"https://doi.org/10.1007/s00493-019-4086-0\">10.1007/s00493-019-4086-0</a>.","ista":"Kwan MA, Letzter S, Sudakov B, Tran T. 2020. Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. 40(2), 283–305."},"article_processing_charge":"No","publication_identifier":{"issn":["0209-9683"],"eissn":["1439-6912"]},"scopus_import":"1","volume":40,"date_published":"2020-04-01T00:00:00Z","quality_controlled":"1"}