{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NCVFJDEMCIWAQOAB6WKH76FT6A","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"60981e83ad1f65a39d6eba9b90bf41020f40e6ba79532cb5a4500d24699a0b19","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-10T03:19:42Z","title_canon_sha256":"f95e9ab582d8ee0dcde0f893be3698ede5ff5eacf0f3caa776373ef3cd25ef88"},"schema_version":"1.0","source":{"id":"1110.1915","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1915","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1915v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1915","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"NCVFJDEMCIWA","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NCVFJDEMCIWAQOAB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NCVFJDEM","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:640cabdd4a57be232301fd69d0ace35cd709dc8e9da2347c4beacf5993b4541e","target":"graph","created_at":"2026-05-18T04:11:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A vertex-colored graph $G$ is {\\it rainbow vertex-connected} if any pair of vertices in $G$ are connected by a path whose internal vertices have distinct colors, which was introduced by Krivelevich and Yuster. The {\\it rainbow vertex-connection number} 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 a previous paper we showed that it is NP-Complete to decide whether a given graph $G$ has $rvc(G)=2$. In this paper we show that for every integer $k\\geq 2$, deciding whether $rvc(G)\\leq k$ is NP-Hard.","authors_text":"Huishu Lian, Lily Chen, Xueliang Li","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-10T03:19:42Z","title":"Further hardness results on the rainbow vertex-connection number of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1915","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c13279fdb56120166abc9595fd6ca1d6ba95fe36df4064bcdde77efbccc83d14","target":"record","created_at":"2026-05-18T04:11:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"60981e83ad1f65a39d6eba9b90bf41020f40e6ba79532cb5a4500d24699a0b19","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-10T03:19:42Z","title_canon_sha256":"f95e9ab582d8ee0dcde0f893be3698ede5ff5eacf0f3caa776373ef3cd25ef88"},"schema_version":"1.0","source":{"id":"1110.1915","kind":"arxiv","version":1}},"canonical_sha256":"68aa548c8c122c083801f5947ff8b3f0045d1d1976f0122b9c48dcbb641bbadb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68aa548c8c122c083801f5947ff8b3f0045d1d1976f0122b9c48dcbb641bbadb","first_computed_at":"2026-05-18T04:11:19.326580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.326580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45FCRMvMb/fHOzVxQjQPu9ZODSN6TEOheJfZ8Fm+YXF9UIUNDWYrkTf1PPCCiQ4QouV5+t29ROBizxXy60JgAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.327043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1915","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c13279fdb56120166abc9595fd6ca1d6ba95fe36df4064bcdde77efbccc83d14","sha256:640cabdd4a57be232301fd69d0ace35cd709dc8e9da2347c4beacf5993b4541e"],"state_sha256":"75cf38c0ce45f6759d0f56131e28e0e9f11f4c76ca53b438d399888dfe16afd6"}