{"paper":{"title":"Loose Hamiltonian cycles forced by large $(k-2)$-degree - approximate version","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fabian Schulenburg, Guilherme Oliveira Mota, Jakob Schnitzer, Josefran de Oliveira Bastos, Mathias Schacht","submitted_at":"2016-03-14T09:53:01Z","abstract_excerpt":"We prove that for all $k\\geq 4$ and $1\\leq\\ell<k/2$, every $k$-uniform hypergraph $\\mathcal{H}$ on $n$ vertices with $\\delta_{k-2}(\\mathcal{H})\\geq\\left(\\frac{4(k-\\ell)-1}{4(k-\\ell)^2}+o(1)\\right)\\binom{n}{2}$ contains a Hamiltonian $\\ell$-cycle if $k-\\ell$ divides $n$. This degree condition is asymptotically best possible. The case $k=3$ was addressed earlier by Bu{\\ss} et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04180","kind":"arxiv","version":2},"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"}