{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T02:21:33Z","timestamp":1774232493279,"version":"3.50.1"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T00:00:00Z","timestamp":1764806400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2026,3]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Recent work showing the existence of conflict-free almost-perfect hypergraph matchings has found many applications. We show that, assuming certain simple degree and codegree conditions on the hypergraph\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100291_inline1.png\"\/>\n                        <jats:tex-math>$ \\mathcal{H}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    and the conflicts to be avoided, a conflict-free almost-perfect matching can be extended to one covering all vertices in a particular subset of\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548325100291_inline2.png\"\/>\n                        <jats:tex-math>$ V(\\mathcal{H})$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , by using an additional set of edges; in particular, we ensure that our matching avoids all additional conflicts, which may consist of both old and new edges. This setup is useful for various applications in design theory and Ramsey theory. For example, our main result provides a crucial tool in the recent proof of the high-girth existence conjecture due to Delcourt and Postle. It also provides a black box which encapsulates many long and tedious calculations, greatly simplifying the proofs of results in generalised Ramsey theory.\n                  <\/jats:p>","DOI":"10.1017\/s0963548325100291","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T04:07:52Z","timestamp":1764821272000},"page":"230-254","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Conflict-free hypergraph matchings and coverings"],"prefix":"10.1017","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8539-9641","authenticated-orcid":false,"given":"Felix","family":"Joos","sequence":"first","affiliation":[{"name":"Universit\u00e4t Heidelberg"}]},{"given":"Dhruv","family":"Mubayi","sequence":"additional","affiliation":[{"name":"University of Illinois Chicago"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-7663-1705","authenticated-orcid":false,"given":"Zak","family":"Smith","sequence":"additional","affiliation":[{"name":"Universit\u00e4t Heidelberg"}]}],"member":"56","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"S0963548325100291_ref15","doi-asserted-by":"crossref","unstructured":"[15] Joos, F , Mubayi, D and Smith, Z (2024). Conflict-free hypergraph matchings and coverings,\u00a0arXiv:2407.18144.","DOI":"10.1017\/S0963548325100291"},{"key":"S0963548325100291_ref8","unstructured":"[8] Delcourt, M and Postle, L (2024). Proof of the high girth existence conjecture via refined absorption, arXiv:2402.17856."},{"key":"S0963548325100291_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(77)90044-9"},{"key":"S0963548325100291_ref7","unstructured":"[7] Delcourt, M and Postle, L (2022). Finding an almost perfect matching in a hypergraph avoiding forbidden submatchings, arXiv:2204.08981."},{"key":"S0963548325100291_ref9","unstructured":"[9] Delcourt, M and Postle, L (2024). Refined absorption: A new proof of the existence conjecture, arXiv:2402.17855."},{"key":"S0963548325100291_ref3","unstructured":"[3] Bennett, P , Heath, E and Zerbib, S (2023). Edge-coloring a graph $g$ so that every copy of a graph $h$ has an odd color class,\u00a0arXiv:2307.01314."},{"key":"S0963548325100291_ref6","unstructured":"[6] Delcourt, M , Kelly, T and Postle, L (2024). Thresholds for $(n,q,2)$ -steiner systems via refined absorption, arXiv: 2402.17858."},{"key":"S0963548325100291_ref13","unstructured":"[13] Gomez-Leos, E , Heath, E , Parker, A , Schwieder, C and Zerbib, S (2023). New bounds on $f(n,5,8)$ , arXiv:2308.16365."},{"key":"S0963548325100291_ref14","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/16413"},{"key":"S0963548325100291_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(89)90074-5"},{"key":"S0963548325100291_ref4","unstructured":"[4] Brown, W , Erd\u0151s, P and S\u00f3s, V (1973). Some extremal problems on $ r$ -graphs.\u00a0New directions in the theory of graphs , 53\u201363."},{"key":"S0963548325100291_ref10","first-page":"609","article-title":"Problems and results on 3-chromatic hypergraphs and some related questions","volume":"10","author":"Erd\u0151s","year":"1975","journal-title":"Infin. Finite Sets"},{"key":"S0963548325100291_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/S0195-6698(85)80045-7"},{"key":"S0963548325100291_ref12","doi-asserted-by":"publisher","DOI":"10.1112\/jlms.12899"},{"key":"S0963548325100291_ref16","unstructured":"[16] Lane, A and Morrison, N (2024). Generalized ramsey numbers via conflict-free hypergraph matchings, arXiv: 2405.16653."},{"key":"S0963548325100291_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2024.07.001"},{"key":"S0963548325100291_ref1","unstructured":"[1] Bal, D , Bennett, P , Heath, E and Zerbib, S (2024). Generalized ramsey numbers of cycles, paths and hypergraphs, arXiv:2405.15904."},{"key":"S0963548325100291_ref5","unstructured":"[5] Delcourt, M , Kelly, T and Postle, L (2024). Clique decompositions in random graphs via refined absorption, arXiv: 2402.17857."}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548325100291","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T08:53:47Z","timestamp":1771404827000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548325100291\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,4]]},"references-count":18,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["S0963548325100291"],"URL":"https:\/\/doi.org\/10.1017\/s0963548325100291","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,4]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}