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This gives a topological extension of Dirac\u2019s theorem and asymptotically confirms a conjecture of Georgakopoulos, Haslegrave, Montgomery, and Narayanan. Unlike typical results in the area, our proof does not rely on the Absorption Method, the Regularity Lemma or the Blow-up Lemma. Instead, we use a recently introduced framework that is based on covering the vertex set of the host graph with a family of complete blow-ups.<\/jats:p>","DOI":"10.1007\/s00493-025-00169-9","type":"journal-article","created":{"date-parts":[[2025,8,7]],"date-time":"2025-08-07T07:14:29Z","timestamp":1754550869000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Spanning Spheres in Dirac Hypergraphs"],"prefix":"10.1007","volume":"45","author":[{"given":"Freddie","family":"Illingworth","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Richard","family":"Lang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alp","family":"M\u00fcyesser","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Olaf","family":"Parczyk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amedeo","family":"Sgueglia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,8,7]]},"reference":[{"issue":"3","key":"169_CR1","doi-asserted-by":"publisher","first-page":"1525","DOI":"10.1137\/20M1336989","volume":"35","author":"Jozsef Balogh","year":"2021","unstructured":"Balogh, J., Lemons, N., Palmer, C.: Maximum size intersecting families of bounded minimum positive co-degree. 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