{"paper":{"title":"The Gyori-Lovasz theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Hoyer, Robin Thomas","submitted_at":"2016-05-05T02:12:01Z","abstract_excerpt":"Gyori and Lovasz independently proved the following beautiful theorem. Let $k\\ge2$ be an integer, let $G$ be a $k$-connected graph on $n$ vertices, let $v_1,v_2,\\ldots,v_k$ be distinct vertices of $G$ and let $n_1,n_2,\\ldots,n_k$ be positive integers with $n_1+n_2+\\cdots+n_k=n$. Then $G$ has disjoint connected subgraphs $G_1,G_2,\\ldots,G_k$ such that for $i=1,2,\\ldots,k$ the graph $G_i$ has $n_i$ vertices and $v_i\\in V(G_i)$. We give a self-contained exposition of Gyori's proof."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01474","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"}