{"paper":{"title":"Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"E. Bu\\ss, H. H\\`an, M. Schacht","submitted_at":"2016-03-14T20:41:33Z","abstract_excerpt":"We investigate minimum vertex degree conditions for $3$-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which only consecutive edges intersect and these intersections consist of precisely one vertex.\n  We prove that every $3$-uniform $n$-vertex ($n$ even) hypergraph $\\mathcal{H}$ with minimum vertex degree $\\delta_1(\\mathcal{H})\\geq \\left(\\frac7{16}+o(1)\\right)\\binom{n}{2}$ contains a loose Hamilton cycle. This bound is asymptotically best possible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04462","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"}