{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T11:03:47Z","timestamp":1768734227459,"version":"3.49.0"},"reference-count":44,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T00:00:00Z","timestamp":1602460800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We employ the absorbing-path method in order to prove two results regarding the emergence of tight Hamilton cycles in the so-called <jats:italic>two-path<\/jats:italic> or <jats:italic>cherry<\/jats:italic>-quasirandom 3-graphs.<\/jats:p><jats:p>Our first result asserts that for any fixed real <jats:italic>\u03b1<\/jats:italic> &gt; 0, cherry-quasirandom 3-graphs of sufficiently large order <jats:italic>n<\/jats:italic> having minimum 2-degree at least <jats:italic>\u03b1<\/jats:italic>(<jats:italic>n<\/jats:italic> \u2013 2) have a tight Hamilton cycle.<\/jats:p><jats:p>Our second result concerns the minimum 1-degree sufficient for such 3-graphs to have a tight Hamilton cycle. Roughly speaking, we prove that for every <jats:italic>d<\/jats:italic>, <jats:italic>\u03b1<\/jats:italic> &gt; 0 satisfying <jats:italic>d<\/jats:italic> + <jats:italic>\u03b1<\/jats:italic> &gt; 1, any sufficiently large <jats:italic>n<\/jats:italic>-vertex such 3-graph <jats:italic>H<\/jats:italic> of density <jats:italic>d<\/jats:italic> and minimum 1-degree at least <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548320000486_inline1.png\"\/><jats:tex-math>$\\alpha \\left({\\matrix{{n - 1} \\cr 2 \\cr } } \\right)$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> has a tight Hamilton cycle.<\/jats:p>","DOI":"10.1017\/s0963548320000486","type":"journal-article","created":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T07:32:53Z","timestamp":1602487973000},"page":"412-443","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["Tight Hamilton cycles in cherry-quasirandom 3-uniform hypergraphs"],"prefix":"10.1017","volume":"30","author":[{"given":"Elad","family":"Aigner-Horev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gil","family":"Levy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"S0963548320000486_ref1","doi-asserted-by":"crossref","DOI":"10.37236\/7537","article-title":"Quasirandomness in hypergraphs.","volume":"25","author":"Aigner-Horev","year":"2018","journal-title":"Electron. 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