{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:53JVP26Z4BSYEIWNMBD2VUWLJX","short_pith_number":"pith:53JVP26Z","schema_version":"1.0","canonical_sha256":"eed357ebd9e0658222cd6047aad2cb4dd1b80b44524b19c677cf8d5f7c8d2749","source":{"kind":"arxiv","id":"1110.5736","version":1},"attestation_state":"computed","paper":{"title":"The rainbow connection number of 2-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ingo Schiermeyer, Jan Ekstein, Maria Koch, P\\v{r}emysl Holub, Stephan Matos Camacho, Tom\\'a\\v{s} Kaiser, Zden\\v{e}k Ryj\\'a\\v{c}ek","submitted_at":"2011-10-26T08:40:31Z","abstract_excerpt":"The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most the ceiling of n/2. The bound is optimal."},"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":"1110.5736","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-10-26T08:40:31Z","cross_cats_sorted":[],"title_canon_sha256":"980e9ead127d2076ab79ff7cf7c8a8b0a5ff42293968019a2753022b1b74d734","abstract_canon_sha256":"a023c5df96330028a99501f5ecba5f1877252e1b261501917942a34579e79f4e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:11.443560Z","signature_b64":"IXP5FKQrZlvCRB3ugSrwQaUJqW1gBAya+NDVLtyQ/pPL5NAWjnxLW1jLGdDbCF6eS9cRZCI18SEug5zMxVY+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eed357ebd9e0658222cd6047aad2cb4dd1b80b44524b19c677cf8d5f7c8d2749","last_reissued_at":"2026-05-18T04:10:11.442726Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:11.442726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The rainbow connection number of 2-connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ingo Schiermeyer, Jan Ekstein, Maria Koch, P\\v{r}emysl Holub, Stephan Matos Camacho, Tom\\'a\\v{s} Kaiser, Zden\\v{e}k Ryj\\'a\\v{c}ek","submitted_at":"2011-10-26T08:40:31Z","abstract_excerpt":"The rainbow connection number of a graph G is the least number of colours in a (not necessarily proper) edge-colouring of G such that every two vertices are joined by a path which contains no colour twice. Improving a result of Caro et al., we prove that the rainbow connection number of every 2-connected graph with n vertices is at most the ceiling of n/2. The bound is optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5736","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":"1110.5736","created_at":"2026-05-18T04:10:11.442856+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.5736v1","created_at":"2026-05-18T04:10:11.442856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5736","created_at":"2026-05-18T04:10:11.442856+00:00"},{"alias_kind":"pith_short_12","alias_value":"53JVP26Z4BSY","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"53JVP26Z4BSYEIWN","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"53JVP26Z","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/53JVP26Z4BSYEIWNMBD2VUWLJX","json":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX.json","graph_json":"https://pith.science/api/pith-number/53JVP26Z4BSYEIWNMBD2VUWLJX/graph.json","events_json":"https://pith.science/api/pith-number/53JVP26Z4BSYEIWNMBD2VUWLJX/events.json","paper":"https://pith.science/paper/53JVP26Z"},"agent_actions":{"view_html":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX","download_json":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX.json","view_paper":"https://pith.science/paper/53JVP26Z","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.5736&json=true","fetch_graph":"https://pith.science/api/pith-number/53JVP26Z4BSYEIWNMBD2VUWLJX/graph.json","fetch_events":"https://pith.science/api/pith-number/53JVP26Z4BSYEIWNMBD2VUWLJX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX/action/storage_attestation","attest_author":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX/action/author_attestation","sign_citation":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX/action/citation_signature","submit_replication":"https://pith.science/pith/53JVP26Z4BSYEIWNMBD2VUWLJX/action/replication_record"}},"created_at":"2026-05-18T04:10:11.442856+00:00","updated_at":"2026-05-18T04:10:11.442856+00:00"}