{"paper":{"title":"On directed versions of the Hajnal--Szemer\\'edi theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrew Treglown","submitted_at":"2014-06-12T13:11:38Z","abstract_excerpt":"We say that a (di)graph $G$ has a perfect $H$-packing if there exists a set of vertex-disjoint copies of $H$ which cover all the vertices in $G$. The seminal Hajnal--Szemer\\'edi theorem characterises the minimum degree that ensures a graph $G$ contains a perfect $K_r$-packing. In this paper we prove the following analogue for directed graphs: Suppose that $T$ is a tournament on $r$ vertices and $G$ is a digraph of sufficiently large order $n$ where $r$ divides $n$. If $G$ has minimum in- and outdegree at least $ (1-1/r)n$ then $G$ contains a perfect $T$-packing. In the case when $T$ is a cycli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3229","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"}