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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1605.01474","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-05T02:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"781d2ffab848b484322555f555858a4e0efcde4224acd37000d75bb67fac4dbf","abstract_canon_sha256":"3e0d256d2e59d3241951cf547b3653b4bb6b4a2af238450a267cf7cead7c940e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:58.904442Z","signature_b64":"jji8NZpbAv7PYcSDn2yshL2+pMK78ZUPYIw7wHgYdTRpQ7okIwwaHvNw+poPzCia3Ekfsfq2zpGGAVe1YhkFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fa790670b11a2e20b345a816e85d806b4a1a9ace0b07b3f5b73cd2269bf4cf0","last_reissued_at":"2026-05-18T01:11:58.904008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:58.904008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.01474","created_at":"2026-05-18T01:11:58.904079+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01474v2","created_at":"2026-05-18T01:11:58.904079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01474","created_at":"2026-05-18T01:11:58.904079+00:00"},{"alias_kind":"pith_short_12","alias_value":"T6TZAZYLCGRO","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"T6TZAZYLCGROECZU","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"T6TZAZYL","created_at":"2026-05-18T12:30:44.179134+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2","json":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2.json","graph_json":"https://pith.science/api/pith-number/T6TZAZYLCGROECZULKAW5BOYA2/graph.json","events_json":"https://pith.science/api/pith-number/T6TZAZYLCGROECZULKAW5BOYA2/events.json","paper":"https://pith.science/paper/T6TZAZYL"},"agent_actions":{"view_html":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2","download_json":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2.json","view_paper":"https://pith.science/paper/T6TZAZYL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01474&json=true","fetch_graph":"https://pith.science/api/pith-number/T6TZAZYLCGROECZULKAW5BOYA2/graph.json","fetch_events":"https://pith.science/api/pith-number/T6TZAZYLCGROECZULKAW5BOYA2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2/action/storage_attestation","attest_author":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2/action/author_attestation","sign_citation":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2/action/citation_signature","submit_replication":"https://pith.science/pith/T6TZAZYLCGROECZULKAW5BOYA2/action/replication_record"}},"created_at":"2026-05-18T01:11:58.904079+00:00","updated_at":"2026-05-18T01:11:58.904079+00:00"}