{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T15:43:55Z","timestamp":1750693435897},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"06","license":[{"start":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T00:00:00Z","timestamp":1561593600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let<jats:italic>r<\/jats:italic>\u2a7e 2 be a fixed constant and let<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:href=\"S0963548319000051_inline1\" xlink:type=\"simple\" \/><jats:tex-math>$ {\\cal H} $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>be an<jats:italic>r<\/jats:italic>-uniform,<jats:italic>D<\/jats:italic>-regular hypergraph on<jats:italic>N<\/jats:italic>vertices. Assume further that<jats:italic>D<\/jats:italic>\u2192 \u221e as<jats:italic>N<\/jats:italic>\u2192 \u221e and that degrees of pairs of vertices in<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:href=\"S0963548319000051_inline2\" xlink:type=\"simple\" \/><jats:tex-math>$ {\\cal H} $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>are at most<jats:italic>L<\/jats:italic>where<jats:italic>L<\/jats:italic>=<jats:italic>D\/<\/jats:italic>( log<jats:italic>N<\/jats:italic>)<jats:sup><jats:italic>\u03c9<\/jats:italic>(1)<\/jats:sup>. We consider the random greedy algorithm for forming a matching in<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:href=\"S0963548319000051_inline3\" xlink:type=\"simple\" \/><jats:tex-math>$ {\\cal H} $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. We choose a matching at random by iteratively choosing edges uniformly at random to be in the matching and deleting all edges that share at least one vertex with a chosen edge before moving on to the next choice. This process terminates when there are no edges remaining in the graph. We show that with high probability the proportion of vertices of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:href=\"S0963548319000051_inline4\" xlink:type=\"simple\" \/><jats:tex-math>$ {\\cal H} $<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>that are not saturated by the final matching is at most (<jats:italic>L<\/jats:italic>\/<jats:italic>D<\/jats:italic>)<jats:sup>(1\/(2(<jats:italic>r<\/jats:italic>\u22121)))+<jats:italic>o<\/jats:italic>(1)<\/jats:sup>. This point is a natural barrier in the analysis of the random greedy hypergraph matching process.<\/jats:p>","DOI":"10.1017\/s0963548319000051","type":"journal-article","created":{"date-parts":[[2019,6,27]],"date-time":"2019-06-27T10:59:31Z","timestamp":1561633171000},"page":"816-825","source":"Crossref","is-referenced-by-count":5,"title":["A natural barrier in random greedy hypergraph matching"],"prefix":"10.1017","volume":"28","author":[{"given":"Patrick","family":"Bennett","sequence":"first","affiliation":[]},{"given":"Tom","family":"Bohman","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2019,6,27]]},"reference":[{"key":"S0963548319000051_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90074-5"},{"key":"S0963548319000051_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80023-8"},{"key":"S0963548319000051_ref7","doi-asserted-by":"crossref","DOI":"10.37236\/1296","volume":"4","author":"Grable","year":"1997","journal-title":"Electron. 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