{"paper":{"title":"Transitive Triangle Tilings in Oriented Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Allan Lo, J\\'ozsef Balogh, Theodore Molla","submitted_at":"2014-01-02T15:58:09Z","abstract_excerpt":"In this paper, we prove an analogue of Corr\\'adi and Hajnal's classical theorem. There exists $n_0$ such that for every $n \\in 3\\mathbb{Z}$ when $n \\ge n_0$ the following holds. If $G$ is an oriented graph on $n$ vertices and every vertex has both indegree and outdegree at least $7n/18$, then $G$ contains a perfect transitive triangle tiling, which is a collection of vertex-disjoint transitive triangles covering every vertex of $G$. This result is best possible, as, for every $n \\in 3\\mathbb{Z}$, there exists an oriented graph $G$ on $n$ vertices without a perfect transitive triangle tiling in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0460","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"}