{"paper":{"title":"Monochromatic cycle partitions of graphs with large minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Louis DeBiasio, Luke Nelsen","submitted_at":"2014-09-05T17:07:07Z","abstract_excerpt":"Lehel conjectured that in every $2$-coloring of the edges of $K_n$, there is a vertex disjoint red and blue cycle which span $V(K_n)$. \\L uczak, R\\\"odl, and Szemer\\'edi proved Lehel's conjecture for large $n$, Allen gave a different proof for large $n$, and finally Bessy and Thomass\\'e gave a proof for all $n$.\n  Balogh, Bar\\'at, Gerbner, Gy\\'arf\\'as, and S\\'ark\\\"ozy proposed a significant strengthening of Lehel's conjecture where $K_n$ is replaced by any graph $G$ with $\\delta(G)> 3n/4$; if true, this minimum degree condition is essentially best possible. We prove that their conjecture holds "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1874","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"}