{"article_processing_charge":"No","acknowledgement":"We thank the referees for extensive comments which helped improve the paper substantially.\r\nThe first author was supported in part by NSF grants DMS-1954395 and DMS-1953799. The second author was supported by NSF grant DMS-1953990. The third author was supported by NSF grant DMS180052. The fourth and fifth authors were both supported by NSF Graduate Research Fellowship Program DGE-1745302.","month":"12","date_updated":"2024-07-15T08:06:05Z","title":"Friendly bisections of random graphs","type":"journal_article","citation":{"apa":"Ferber, A., Kwan, M. A., Narayanan, B., Sah, A., &#38; Sawhney, M. (2022). Friendly bisections of random graphs. <i>Communications of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/cams/13\">https://doi.org/10.1090/cams/13</a>","chicago":"Ferber, Asaf, Matthew Alan Kwan, Bhargav Narayanan, Ashwin Sah, and Mehtaab Sawhney. “Friendly Bisections of Random Graphs.” <i>Communications of the American Mathematical Society</i>. American Mathematical Society, 2022. <a href=\"https://doi.org/10.1090/cams/13\">https://doi.org/10.1090/cams/13</a>.","mla":"Ferber, Asaf, et al. “Friendly Bisections of Random Graphs.” <i>Communications of the American Mathematical Society</i>, vol. 2, no. 10, American Mathematical Society, 2022, pp. 380–416, doi:<a href=\"https://doi.org/10.1090/cams/13\">10.1090/cams/13</a>.","ama":"Ferber A, Kwan MA, Narayanan B, Sah A, Sawhney M. Friendly bisections of random graphs. <i>Communications of the American Mathematical Society</i>. 2022;2(10):380-416. doi:<a href=\"https://doi.org/10.1090/cams/13\">10.1090/cams/13</a>","ieee":"A. Ferber, M. A. Kwan, B. Narayanan, A. Sah, and M. Sawhney, “Friendly bisections of random graphs,” <i>Communications of the American Mathematical Society</i>, vol. 2, no. 10. American Mathematical Society, pp. 380–416, 2022.","short":"A. Ferber, M.A. Kwan, B. Narayanan, A. Sah, M. Sawhney, Communications of the American Mathematical Society 2 (2022) 380–416.","ista":"Ferber A, Kwan MA, Narayanan B, Sah A, Sawhney M. 2022. Friendly bisections of random graphs. Communications of the American Mathematical Society. 2(10), 380–416."},"date_created":"2024-05-29T06:13:37Z","has_accepted_license":"1","status":"public","article_type":"original","department":[{"_id":"MaKw"}],"oa_version":"Published Version","publication_identifier":{"issn":["2692-3688"]},"abstract":[{"lang":"eng","text":"Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random graph 𝔾(𝑛, 1/2) admits a friendly bisection of its vertex set, i.e., a\r\npartition of its vertex set into two parts whose sizes differ by at most one in which\r\n𝑛 − 𝑜(𝑛) vertices have more neighbours in their own part as across. Our proof is constructive, and in the process, we develop a new method to study stochastic processes\r\ndriven by degree information in random graphs; this involves combining enumeration\r\ntechniques with an abstract second moment argument."}],"year":"2022","ddc":["500"],"issue":"10","publisher":"American Mathematical Society","external_id":{"arxiv":["2105.13337"]},"_id":"17077","volume":2,"author":[{"last_name":"Ferber","full_name":"Ferber, Asaf","first_name":"Asaf"},{"first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","full_name":"Kwan, Matthew Alan","last_name":"Kwan"},{"first_name":"Bhargav","full_name":"Narayanan, Bhargav","last_name":"Narayanan"},{"full_name":"Sah, Ashwin","last_name":"Sah","first_name":"Ashwin"},{"first_name":"Mehtaab","full_name":"Sawhney, Mehtaab","last_name":"Sawhney"}],"doi":"10.1090/cams/13","day":"20","publication_status":"published","publication":"Communications of the American Mathematical Society","date_published":"2022-12-20T00:00:00Z","file":[{"date_created":"2024-07-12T12:55:02Z","success":1,"checksum":"719861e76f5bce3d0362d8171daa26fc","file_id":"17230","access_level":"open_access","relation":"main_file","file_name":"2022_CommAMS_Ferber.pdf","date_updated":"2024-07-12T12:55:02Z","file_size":335965,"creator":"cchlebak","content_type":"application/pdf"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"380-416","file_date_updated":"2024-07-12T12:55:02Z","tmp":{"name":"Creative Commons Attribution 3.0 Unported (CC BY 3.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/3.0/legalcode","short":"CC BY (3.0)"},"oa":1,"corr_author":"1","language":[{"iso":"eng"}],"quality_controlled":"1","intvolume":"         2"}