{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4V2IDGBBQT6BCDJRCWZ3VETY2H","short_pith_number":"pith:4V2IDGBB","schema_version":"1.0","canonical_sha256":"e57481982184fc110d3115b3ba9278d1f0a6092452ddf56587cdc44b63d779c0","source":{"kind":"arxiv","id":"1101.3126","version":1},"attestation_state":"computed","paper":{"title":"The complexity of determining the rainbow vertex-connection of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Lily Chen, Xueliang Li, Yongtang Shi","submitted_at":"2011-01-17T05:44:18Z","abstract_excerpt":"A vertex-colored graph is {\\it rainbow vertex-connected} if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\\it rainbow vertex-connection} of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. In this paper, we study the computational complexity of vertex-rainbow connection of graphs and prove that computing $rvc(G)$ is NP-Hard. Moreover, we show that it is already NP-Complete to decide whether $rvc(G)=2$. We also p"},"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":"1101.3126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-17T05:44:18Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"49de11e077efc115a677e902951db7a4e70be14010bb9d35526f24af3db09ea0","abstract_canon_sha256":"9aed681f690298d964b4e21c570afda90b5cfc24ecaf5fca3a03cc43484b2d69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:30.454446Z","signature_b64":"Uu5yVd+RizlBcULYed/I+okyh922iDdeEHwXAp88QW7Ldzp5SGgNWiVvn6WwqAAFD/KalIQ1jgKn9Hz/ALw5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e57481982184fc110d3115b3ba9278d1f0a6092452ddf56587cdc44b63d779c0","last_reissued_at":"2026-05-18T04:31:30.454038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:30.454038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complexity of determining the rainbow vertex-connection of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Lily Chen, Xueliang Li, Yongtang Shi","submitted_at":"2011-01-17T05:44:18Z","abstract_excerpt":"A vertex-colored graph is {\\it rainbow vertex-connected} if any two vertices are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\\it rainbow vertex-connection} of a connected graph $G$, denoted by $rvc(G)$, is the smallest number of colors that are needed in order to make $G$ rainbow vertex-connected. In this paper, we study the computational complexity of vertex-rainbow connection of graphs and prove that computing $rvc(G)$ is NP-Hard. Moreover, we show that it is already NP-Complete to decide whether $rvc(G)=2$. We also p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3126","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1101.3126","created_at":"2026-05-18T04:31:30.454100+00:00"},{"alias_kind":"arxiv_version","alias_value":"1101.3126v1","created_at":"2026-05-18T04:31:30.454100+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.3126","created_at":"2026-05-18T04:31:30.454100+00:00"},{"alias_kind":"pith_short_12","alias_value":"4V2IDGBBQT6B","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4V2IDGBBQT6BCDJR","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4V2IDGBB","created_at":"2026-05-18T12:26:20.644004+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/4V2IDGBBQT6BCDJRCWZ3VETY2H","json":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H.json","graph_json":"https://pith.science/api/pith-number/4V2IDGBBQT6BCDJRCWZ3VETY2H/graph.json","events_json":"https://pith.science/api/pith-number/4V2IDGBBQT6BCDJRCWZ3VETY2H/events.json","paper":"https://pith.science/paper/4V2IDGBB"},"agent_actions":{"view_html":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H","download_json":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H.json","view_paper":"https://pith.science/paper/4V2IDGBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1101.3126&json=true","fetch_graph":"https://pith.science/api/pith-number/4V2IDGBBQT6BCDJRCWZ3VETY2H/graph.json","fetch_events":"https://pith.science/api/pith-number/4V2IDGBBQT6BCDJRCWZ3VETY2H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H/action/storage_attestation","attest_author":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H/action/author_attestation","sign_citation":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H/action/citation_signature","submit_replication":"https://pith.science/pith/4V2IDGBBQT6BCDJRCWZ3VETY2H/action/replication_record"}},"created_at":"2026-05-18T04:31:30.454100+00:00","updated_at":"2026-05-18T04:31:30.454100+00:00"}