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The case  is the classical anti\u2010Ramsey problem proposed by Erd\u0151s\u2013Simonovits\u2013S\u00f3s [1]. When  is a single edge, this becomes the rainbow matching problem introduced by Schiermeyer [2] and \u00d6zkahya\u2013Young [3]. We conduct a systematic study of  for the case when  is much smaller than . Our first main result provides a reduction of  to  when  is bounded and smooth, two properties satisfied by most previously studied hypergraphs. Complementing the first result, the second main result, which utilizes gaps between Tur\u00e1n numbers, determines  for relatively smaller . Together, these two results determine  for a large class of hypergraphs. Additionally, the latter result has the advantage of being applicable to hypergraphs with unknown Tur\u00e1n densities, such as the famous tetrahedron .<\/jats:p>","DOI":"10.1002\/jgt.23282","type":"journal-article","created":{"date-parts":[[2025,7,23]],"date-time":"2025-07-23T08:14:27Z","timestamp":1753258467000},"page":"457-467","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Tight Bounds for Rainbow Partial F\u2010Tiling in Edge\u2010Colored Complete Hypergraphs"],"prefix":"10.1002","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5537-5707","authenticated-orcid":false,"given":"Jinghua","family":"Deng","sequence":"first","affiliation":[{"name":"Center for Discrete Mathematics Fuzhou University Fuzhou Fujian China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianfeng","family":"Hou","sequence":"additional","affiliation":[{"name":"Center for Discrete Mathematics Fuzhou University Fuzhou Fujian China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xizhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Mathematics Institute and DIMAP University of Warwick Coventry England UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caihong","family":"Yang","sequence":"additional","affiliation":[{"name":"Center for Discrete Mathematics Fuzhou University Fuzhou Fujian China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,7,23]]},"reference":[{"key":"e_1_2_11_2_1","unstructured":"P.Erd\u0151s M.Simonovits andV. 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