{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T22:59:21Z","timestamp":1791241161563,"version":"4.1.0"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","funder":[{"DOI":"10.13039\/100006778","name":"Georgia Institute of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006778","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471257"],"award-info":[{"award-number":["11471257"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1600738"],"award-info":[{"award-number":["DMS-1600738"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1600738"],"award-info":[{"award-number":["DMS-1600738"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1954134"],"award-info":[{"award-number":["DMS-1954134"]}],"id":[{"id":"10.13039\/100000001","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>We prove that, for any integers $k,l$ with $k\\ge 3$ and $k\/2&lt;l\\leq k-1$, there exists a positive real $\\mu$ such that, for all sufficiently large integers $m,n$ satisfying $ \\frac{n}{k}-\\mu n\\le m\\le \\frac{n}{k} -1- (1-\\frac{l}{k})\\left\\lceil\\frac{k-l}{2l-k}\\right\\rceil, $ if $H$ is a $k$-uniform hypergraph on $n$ vertices and $\\delta_{l}(H)&gt;{n-l\\choose k-l}-{(n-l)-m\\choose k-l}$, then $H$ has a matching of size $m+1$. This improves upon an earlier result of H\u00e0n, Person, and Schacht for the range $k\/2&lt;l\\leq k-1$. In many cases, our result gives a tight bound on $\\delta_l(H)$ for near perfect matchings (e.g., when $l\\ge 2k\/3$, $n\\equiv r \\pmod k$, $0\\le r&lt;k$, and $r+l\\ge k$, we can take $m=\\lceil n\/k\\rceil -2$). When $k=3$, using an absorbing lemma of H\u00e0n, Person, and Schacht, our proof also implies a result of K\u00fchn, Osthus, and Treglown (and, independently, of Khan) on perfect matchings in 3-uniform hypergraphs.<\/jats:p>","DOI":"10.1137\/19m1300662","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T11:57:11Z","timestamp":1621252631000},"page":"1022-1049","source":"Crossref","is-referenced-by-count":8,"title":["Nearly Perfect Matchings in Uniform Hypergraphs"],"prefix":"10.1137","volume":"35","author":[{"given":"Hongliang","family":"Lu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingxing","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaofan","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2012.02.004"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"N. Alon and J. Spencer,\n                      The Probabilistic Method\n                      , 3rd ed., Wiley Ser. Discrete Math. Optim., Wiley, Hoboken, NJ, 2008.","DOI":"10.1002\/9780470277331"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1090\/S0894-0347-2014-00816-X"},{"key":"atypb4","first-page":"258","volume":"247","author":"Berge C.","year":"1958","journal-title":"C. R. Hebdomadaires Acad. Sci."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1093\/qmath\/27.1.25"},{"key":"atypb6","first-page":"93","volume":"8","author":"Erd\u00f6s P.","year":"1965","journal-title":"Ann. Univ. Sci. Budapest. E\u00f6tv\u00f6s Sect. Math."},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"D. Ellis, N. Keller, and N. Lifshitz,\n                      Stability versions of Erd\u00f6s-Ko-Rado type theorems, via isoperimetry\n                      , J. Eur. Math. Soc. (JEMS), 21 (2019), pp. 3857-3902.","DOI":"10.4171\/jems\/915"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2013.01.008"},{"key":"atypb9","unstructured":"P. Frankl and A. Kupavskii,\n                      The Erd\u00f6s Matching Conjecture and Concentration Inequalities\n                      , preprint,https:\/\/arxiv.org\/abs\/1806.08855v2[math.CO] (2018)."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80045-7"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000613"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/080729657"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1007\/BF01897141"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/10080796X"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20139"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.11.006"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2012.11.005"},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"M. Mitzenmacher and E. Upfal,\n                      Probability and Computing: Randomized Algorithms and Probabilistic Analysis\n                      , Cambridge University Press, Cambridge, 2005.","DOI":"10.1017\/CBO9780511813603"},{"key":"atypb19","first-page":"561","author":"R\u00f6dl V.","year":"2010","journal-title":"Berlin"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2006.05.008"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2008.10.002"},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-014-0562-8"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2012.04.006"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2013.04.008"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Y. Zhao,\n                      Recent advances on dirac-type problems for hypergraphs\n                      , in Recent Trends in Combinatorics, IMA Volumes in Mathematics and its Applications, Vol. 159. Springer, New York, 2016.","DOI":"10.1007\/978-3-319-24298-9_6"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1300662","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:44:18Z","timestamp":1787319858000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1300662"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":25,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1300662"],"URL":"https:\/\/doi.org\/10.1137\/19m1300662","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}