{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T11:49:41Z","timestamp":1782906581299,"version":"3.54.5"},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T00:00:00Z","timestamp":1747353600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a short and simple proof of the celebrated hypergraph container theorem of Balogh\u2013Morris\u2013Samotij and Saxton\u2013Thomason. On a high level, our argument utilises the idea of iteratively taking vertices of largest degree from an independent set and constructing a hypergraph of lower uniformity which preserves independent sets and inherits edge distribution. The original algorithms for constructing containers also remove in each step vertices of high degree, which are not in the independent set. Our modified algorithm postpones this until the end, which surprisingly results in a significantly simplified analysis.<\/jats:p>","DOI":"10.1017\/s0963548325000112","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T04:01:21Z","timestamp":1747368081000},"page":"621-624","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Short proof of the hypergraph container theorem"],"prefix":"10.1017","volume":"34","author":[{"given":"Rajko","family":"Nenadov","sequence":"first","affiliation":[{"name":"University of Auckland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Huy Tuan","family":"Pham","sequence":"additional","affiliation":[{"name":"Institute for Advanced Study"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,5,16]]},"reference":[{"key":"S0963548325000112_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S096354831500022X"},{"key":"S0963548325000112_ref3","first-page":"56","article-title":"An efficient container lemma","volume":"2020","author":"Balogh","year":"2020","journal-title":"Discrete Anal."},{"key":"S0963548325000112_ref8","doi-asserted-by":"publisher","DOI":"10.1007\/s11856-023-2602-9"},{"key":"S0963548325000112_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/14368"},{"key":"S0963548325000112_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2016.05.011"},{"key":"S0963548325000112_ref5","unstructured":"[5] Buci\u0107, M. , Fox, J. and Pham, H. T. (2024) Equivalence between Erd\u0151s-Hajnal and polynomial R\u00f6dl and Nikiforov conjectures, arXiv: 2403.08303."},{"key":"S0963548325000112_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-014-0562-8"},{"key":"S0963548325000112_ref1","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00816-X"},{"key":"S0963548325000112_ref7","doi-asserted-by":"publisher","DOI":"10.4171\/jems\/1442"},{"key":"S0963548325000112_ref2","doi-asserted-by":"crossref","unstructured":"[2] Balogh, J. , Morris, R. and Samotij, W. (2018) The method of hypergraph containers. In Proceedings of the International Congress of Mathematicians 2018, ICM 2018, Rio de Janeiro, Brazil, August 1\u20139, 2018, Vol. IV Invited lectures, World Scientific, Sociedade Brasileira de Matem\u00e1tica (SBM), Brazil, Hackensack, NJ-Rio de Janeiro, pp. 3059\u20133092.","DOI":"10.1142\/9789813272880_0172"},{"key":"S0963548325000112_ref6","unstructured":"[6] Campos, M. and Samotij, W. (2024) Towards an optimal hypergraph container lemma, arXiv: 2408.06617."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548325000112","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T00:12:19Z","timestamp":1757981539000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548325000112\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,16]]},"references-count":11,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["S0963548325000112"],"URL":"https:\/\/doi.org\/10.1017\/s0963548325000112","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5,16]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}