{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:H46AUMLVJAVZUSLZ3KDRWZODYH","short_pith_number":"pith:H46AUMLV","canonical_record":{"source":{"id":"1011.4572","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-20T09:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"0f9ee84af7c84ae97c342a870364d1b2070b0be78d758a56b4c1941b71f1add8","abstract_canon_sha256":"685a16211b6941ba6554df549962edc2b134df7190992bd6c804586a09c857f7"},"schema_version":"1.0"},"canonical_sha256":"3f3c0a3175482b9a4979da871b65c3c1cebadefe0f335e39b32cb7a658461f99","source":{"kind":"arxiv","id":"1011.4572","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:H46AUMLVJAVZUSLZ3KDRWZODYH","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4572","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-11-20T09:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"0f9ee84af7c84ae97c342a870364d1b2070b0be78d758a56b4c1941b71f1add8","abstract_canon_sha256":"685a16211b6941ba6554df549962edc2b134df7190992bd6c804586a09c857f7"},"schema_version":"1.0"},"canonical_sha256":"3f3c0a3175482b9a4979da871b65c3c1cebadefe0f335e39b32cb7a658461f99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:35.871124Z","signature_b64":"KksEhnPOTAEvfL0eId0X8XyOSHdlLyRYB/WvxY1cWJIwJVrfKgHHXG9pvQtOUN2JlR2yWK1/CmDTBjNLrdhgAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f3c0a3175482b9a4979da871b65c3c1cebadefe0f335e39b32cb7a658461f99","last_reissued_at":"2026-05-18T04:32:35.870603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:35.870603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4572","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ja8NdkKs9f1/nP20pu4EY01Zw8AM0fyu3L1MXEqYpL3FseeTNB87ypMBARVp+BZO3/nalFpkXrwcEEiVlfKlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:10:32.920774Z"},"content_sha256":"7e5e028efc519bc1c340c96d2284a140de30c80bb91d98fb42f9adabe1bc89b1","schema_version":"1.0","event_id":"sha256:7e5e028efc519bc1c340c96d2284a140de30c80bb91d98fb42f9adabe1bc89b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:H46AUMLVJAVZUSLZ3KDRWZODYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rainbow connection numbers of complementary graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xueliang Li, Yuefang Sun","submitted_at":"2010-11-20T09:45:13Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4572","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7U+UUIvpwFw9SImOqzSmJ+UiZe5OR3BkN4bCK1bXJRcmnY/sJyH6jmD1+2JIoF7lVtL8luEhlg/4hw5VnYb1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:10:32.921112Z"},"content_sha256":"7a9075119b47cc09083eee9f39649efab3c907aa8dc61516e6cb8870877f308c","schema_version":"1.0","event_id":"sha256:7a9075119b47cc09083eee9f39649efab3c907aa8dc61516e6cb8870877f308c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/bundle.json","state_url":"https://pith.science/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T21:10:32Z","links":{"resolver":"https://pith.science/pith/H46AUMLVJAVZUSLZ3KDRWZODYH","bundle":"https://pith.science/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/bundle.json","state":"https://pith.science/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H46AUMLVJAVZUSLZ3KDRWZODYH/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0iew8CRVHaW+xVRN3x6BY/gNwc9dJuZQvHO9Lt2AsQkpW73k8tnWi2KAhTC9iM0+ZmbLfghNxgYIOiurOZ30Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:10:32.923419Z","bundle_sha256":"21bddf0856c12b78ac726da854ae1615e46b81de1c10230c327d92f5f422ca99"}}