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This answers, in a strong sense, a problem asked by K\\\"uhn and Osthus (originally attributed to Shi). A main ingredient in our proof is an induced variant of Mader's theorem: for every fixed \\(s,\\eta,D\\), every graph \\(J\\) with \\(\\Delta(J)\\le D\\), \\(d(J)>s-2+\\eta\\) and sufficiently large girth contains an induced subdivision of \\(K_s\\).","authors_text":"Peiru Kuang, Yan Wang","cross_cats":[],"headline":"Graphs with minimum degree at least k and girth above a fixed constant contain an induced subdivision of K_{k+1}.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-05-17T01:32:55Z","title":"Induced subdivisions in graphs of large girth"},"references":{"count":36,"internal_anchors":0,"resolved_work":36,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"N. Alon, S. Hoory and N. 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