{"paper":{"title":"Partitioning $2$-coloured complete $k$-uniform hypergraphs into monochromatic $\\ell$-cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maya Stein, Sebastian Bustamante","submitted_at":"2017-11-13T18:30:00Z","abstract_excerpt":"We show that for all $\\ell, k, n$ with $\\ell \\leq k/2$ and $(k-\\ell)$ dividing $n$ the following hypergraph-variant of Lehel's conjecture is true. Every $2$-edge-colouring of the $k$-uniform complete hypergraph $\\mathcal{K}_n^{(k)}$ on $n$ vertices has at most two disjoint monochromatic $\\ell$-cycles in different colours that together cover all but at most $4(k-\\ell)$ vertices. If $\\ell \\leq k/3$, then at most two $\\ell$-cycles cover all but at most $2(k-\\ell)$ vertices. Furthermore, we can cover all vertices with at most $4$ ($3$ if $\\ell\\leq k/3$) disjoint monochromatic $\\ell$-cycles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04748","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"}