{"paper":{"title":"On directed versions of the Corr\\'adi-Hajnal Corollary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Czygrinow, H.A. Kierstead, Theodore Molla","submitted_at":"2013-09-18T01:53:27Z","abstract_excerpt":"For $k \\in \\mathbb N$, Corr\\'adi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $\\delta(G) \\ge 2k$ has a $C_3$-factor, i.e., a partitioning of the vertex set so that each part induces the 3-cycle $C_3$. Wang proved that every directed graph $\\overrightarrow G$ on $3k$ vertices with minimum total degree $\\delta_t(\\overrightarrow G):=\\min_{v\\in V}(deg^-(v)+deg^+(v)) \\ge 3(3k-1)/2$ has a $\\overrightarrow C_3$-factor, where $\\overrightarrow C_3$ is the directed 3-cycle. The degree bound in Wang's result is tight. However, our main result implies that for all integers $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.4520","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"}