{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H46AUMLVJAVZUSLZ3KDRWZODYH","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":"685a16211b6941ba6554df549962edc2b134df7190992bd6c804586a09c857f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-20T09:45:13Z","title_canon_sha256":"0f9ee84af7c84ae97c342a870364d1b2070b0be78d758a56b4c1941b71f1add8"},"schema_version":"1.0","source":{"id":"1011.4572","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4572","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4572v3","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4572","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"H46AUMLVJAVZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H46AUMLVJAVZUSLZ","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H46AUMLV","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:7a9075119b47cc09083eee9f39649efab3c907aa8dc61516e6cb8870877f308c","target":"graph","created_at":"2026-05-18T04:32:35Z","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 path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph $G$ is rainbow connected if there is a rainbow path connecting any two vertices, and the rainbow connection number of $G$, denoted by $rc(G)$, is the minimum number of colors that are needed in order to make $G$ rainbow connected. In this paper, we provide a new approach to investigate the rainbow connection number of a graph $G$ according to some constraints to its complement graph $\\bar{G}$. We first derive that for a connec","authors_text":"Xueliang Li, Yuefang Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-20T09:45:13Z","title":"Rainbow connection numbers of complementary graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4572","kind":"arxiv","version":3},"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":"sha256:7e5e028efc519bc1c340c96d2284a140de30c80bb91d98fb42f9adabe1bc89b1","target":"record","created_at":"2026-05-18T04:32:35Z","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":"685a16211b6941ba6554df549962edc2b134df7190992bd6c804586a09c857f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-20T09:45:13Z","title_canon_sha256":"0f9ee84af7c84ae97c342a870364d1b2070b0be78d758a56b4c1941b71f1add8"},"schema_version":"1.0","source":{"id":"1011.4572","kind":"arxiv","version":3}},"canonical_sha256":"3f3c0a3175482b9a4979da871b65c3c1cebadefe0f335e39b32cb7a658461f99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f3c0a3175482b9a4979da871b65c3c1cebadefe0f335e39b32cb7a658461f99","first_computed_at":"2026-05-18T04:32:35.870603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:35.870603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KksEhnPOTAEvfL0eId0X8XyOSHdlLyRYB/WvxY1cWJIwJVrfKgHHXG9pvQtOUN2JlR2yWK1/CmDTBjNLrdhgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:35.871124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4572","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e5e028efc519bc1c340c96d2284a140de30c80bb91d98fb42f9adabe1bc89b1","sha256:7a9075119b47cc09083eee9f39649efab3c907aa8dc61516e6cb8870877f308c"],"state_sha256":"e2e97c0a566b1428be1404ce6d40a5e6b8d846211a68bbfb89bdef118b80a323"}