{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T15:13:04Z","timestamp":1772809984336,"version":"3.50.1"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T00:00:00Z","timestamp":1602547200000},"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":[[2021,3]]},"abstract":"Abstract<\/jats:title>A k<\/jats:italic>-uniform tight cycle $C_s^k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is a hypergraph on s<\/jats:italic> > k<\/jats:italic> vertices with a cyclic ordering such that every k<\/jats:italic> consecutive vertices under this ordering form an edge. The pair (k<\/jats:italic>, s<\/jats:italic>) is admissible if gcd (k<\/jats:italic>, s<\/jats:italic>) = 1 or k<\/jats:italic> \/ gcd (k<\/jats:italic>,s<\/jats:italic>) is even. We prove that if $s \\ge 2{k^2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and H<\/jats:italic> is a k<\/jats:italic>-uniform hypergraph with minimum codegree at least (1\/2 + o<\/jats:italic>(1))|V<\/jats:italic>(H<\/jats:italic>)|, then every vertex is covered by a copy of $C_s^k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. The bound is asymptotically sharp if (k<\/jats:italic>, s<\/jats:italic>) is admissible. Our main tool allows us to arbitrarily rearrange the order in which a tight path wraps around a complete k<\/jats:italic>-partite k<\/jats:italic>-uniform hypergraph, which may be of independent interest.<\/jats:p>For hypergraphs F<\/jats:italic> and H<\/jats:italic>, a perfect F<\/jats:italic>-tiling in H<\/jats:italic> is a spanning collection of vertex-disjoint copies of F<\/jats:italic>. For $k \\ge 3$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, there are currently only a handful of known F<\/jats:italic>-tiling results when F<\/jats:italic> is k<\/jats:italic>-uniform but not k<\/jats:italic>-partite. If s<\/jats:italic> \u2262 0 mod k<\/jats:italic>, then $C_s^k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is not k<\/jats:italic>-partite. Here we prove an F<\/jats:italic>-tiling result for a family of non-k<\/jats:italic>-partite k<\/jats:italic>-uniform hypergraphs F<\/jats:italic>. Namely, for $s \\ge 5{k^2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, every k<\/jats:italic>-uniform hypergraph H<\/jats:italic> with minimum codegree at least (1\/2 + 1\/(2s<\/jats:italic>) + o<\/jats:italic>(1))|V(H)| has a perfect $C_s^k$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-tiling. Moreover, the bound is asymptotically sharp if k<\/jats:italic> is even and (k<\/jats:italic>, s<\/jats:italic>) is admissible.<\/jats:p>","DOI":"10.1017\/s0963548320000449","type":"journal-article","created":{"date-parts":[[2020,10,13]],"date-time":"2020-10-13T02:24:45Z","timestamp":1602555885000},"page":"288-329","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["Covering and tiling hypergraphs with tight cycles"],"prefix":"10.1017","volume":"30","author":[{"given":"Jie","family":"Han","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allan","family":"Lo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicol\u00e1s","family":"Sanhueza-Matamala","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2020,10,13]]},"reference":[{"key":"S0963548320000449_ref2","unstructured":"[2] Allen, P. , B\u00f6ttcher, J. , Cooley, O. and Mycroft, R. 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