{"paper":{"title":"Powers of tight Hamilton cycles in randomly perturbed hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guilherme Oliveira Mota, Jie Han, Wiebke Bedenknecht, Yoshiharu Kohayakawa","submitted_at":"2018-02-24T19:26:45Z","abstract_excerpt":"For $k\\ge 2$ and $r\\ge 1$ such that $k+r\\ge 4$, we prove that, for any $\\alpha>0$, there exists $\\epsilon>0$ such that the union of an $n$-vertex $k$-graph with minimum codegree $\\left(1-\\binom{k+r-2}{k-1}^{-1}+\\alpha\\right)n$ and a binomial random $k$-graph $\\mathbb{G}^{(k)}(n,p)$ with $p\\ge n^{-\\binom{k+r-2}{k-1}^{-1}-\\epsilon}$ on the same vertex set contains the $r^{\\text{th}}$ power of a tight Hamilton cycle with high probability. This result for $r=1$ was first proved by McDowell and Mycroft."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08900","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}