{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T02:04:10Z","timestamp":1787364250962,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1764123"],"award-info":[{"award-number":["DMS-1764123"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["712036"],"award-info":[{"award-number":["712036"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005302","name":"University of Illinois at Urbana-Champaign","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100005302","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Let $\\mathcal{H}$ be an $r$-uniform hypergraph. The minimum positive co-degree of $\\mathcal{H}$, denoted by $\\delta_{r-1}^+(\\mathcal{H})$, is the minimum $k$ such that if $S$ is an $(r-1)$-set contained in a hyperedge of $\\mathcal{H}$, then $S$ is contained in at least $k$ hyperedges of $\\mathcal{H}$. For $r\\geq k$ fixed and $n$ sufficiently large, we determine the maximum possible size of an intersecting $r$-uniform $n$-vertex hypergraph with minimum positive co-degree $\\delta_{r-1}^+(\\mathcal{H}) \\geq k$ and characterize the unique hypergraph attaining this maximum. This generalizes the Erd\\Hos--Ko--Rado theorem which corresponds to the case $k=1$. Our proof is based on the delta-system method.<\/jats:p>","DOI":"10.1137\/20m1336989","type":"journal-article","created":{"date-parts":[[2021,7,1]],"date-time":"2021-07-01T13:49:51Z","timestamp":1625147391000},"page":"1525-1535","source":"Crossref","is-referenced-by-count":11,"title":["Maximum Size Intersecting Families of Bounded Minimum Positive Co-degree"],"prefix":"10.1137","volume":"35","author":[{"given":"Jozsef","family":"Balogh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nathan","family":"Lemons","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6718-5762","authenticated-orcid":true,"given":"Cory","family":"Palmer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,7,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"R. 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J\u00e1nos Bolyai, 25, North-Holland, Amsterdam, 1981, pp. 177-207."},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01956765"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(83)90081-X"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2017.03.006"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2004.05.003"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2014.09.005"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2019.06.002"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2018.07.005"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-008-0793-9"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2006.11.006"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-007-0755-7"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1336989","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:06:20Z","timestamp":1787321180000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1336989"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1336989"],"URL":"https:\/\/doi.org\/10.1137\/20m1336989","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}