--- _id: '9582' abstract: - lang: eng 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. article_processing_charge: No article_type: original author: - first_name: Matthew Alan full_name: Kwan, Matthew Alan id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3 last_name: Kwan orcid: 0000-0002-4003-7567 - first_name: Shoham full_name: Letzter, Shoham last_name: Letzter - first_name: Benny full_name: Sudakov, Benny last_name: Sudakov - first_name: Tuan full_name: Tran, Tuan last_name: Tran citation: ama: Kwan MA, Letzter S, Sudakov B, Tran T. Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. 2020;40(2):283-305. doi:10.1007/s00493-019-4086-0 apa: Kwan, M. A., Letzter, S., Sudakov, B., & Tran, T. (2020). Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. Springer. https://doi.org/10.1007/s00493-019-4086-0 chicago: Kwan, Matthew Alan, Shoham Letzter, Benny Sudakov, and Tuan Tran. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” Combinatorica. Springer, 2020. https://doi.org/10.1007/s00493-019-4086-0. ieee: M. A. Kwan, S. Letzter, B. Sudakov, and T. Tran, “Dense induced bipartite subgraphs in triangle-free graphs,” Combinatorica, vol. 40, no. 2. Springer, pp. 283–305, 2020. ista: Kwan MA, Letzter S, Sudakov B, Tran T. 2020. Dense induced bipartite subgraphs in triangle-free graphs. Combinatorica. 40(2), 283–305. mla: Kwan, Matthew Alan, et al. “Dense Induced Bipartite Subgraphs in Triangle-Free Graphs.” Combinatorica, vol. 40, no. 2, Springer, 2020, pp. 283–305, doi:10.1007/s00493-019-4086-0. short: M.A. Kwan, S. Letzter, B. Sudakov, T. Tran, Combinatorica 40 (2020) 283–305. date_created: 2021-06-22T06:42:26Z date_published: 2020-04-01T00:00:00Z date_updated: 2023-02-23T14:01:45Z day: '01' doi: 10.1007/s00493-019-4086-0 extern: '1' external_id: arxiv: - '1810.12144' intvolume: ' 40' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1810.12144 month: '04' oa: 1 oa_version: Preprint page: 283-305 publication: Combinatorica publication_identifier: eissn: - 1439-6912 issn: - 0209-9683 publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Dense induced bipartite subgraphs in triangle-free graphs type: journal_article user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf volume: 40 year: '2020' ...