{"paper":{"title":"Minimum vertex degree threshold for $C_4^3$-tiling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jie Han, Yi Zhao","submitted_at":"2013-09-09T15:48:17Z","abstract_excerpt":"We prove that the vertex degree threshold for tiling $\\C_4^3$ (the 3-uniform hypergraph with four vertices and two triples) in a 3-uniform hypergraph on $n\\in 4\\mathbb N$ vertices is $\\binom{n-1}2 - \\binom{\\frac34 n}2+\\frac38n+c$, where $c=1$ if $n\\in 8\\mathbb N$ and $c=-\\frac12$ otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2200","kind":"arxiv","version":4},"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"}