{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:MC4S75QNDTY6L4EOYTTH6LVOLS","short_pith_number":"pith:MC4S75QN","schema_version":"1.0","canonical_sha256":"60b92ff60d1cf1e5f08ec4e67f2eae5cb930c686f29a2dafe45e9f42a01c613b","source":{"kind":"arxiv","id":"1108.1616","version":1},"attestation_state":"computed","paper":{"title":"Colouring Edges with many Colours in Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jaroslav Nesetril (KAM), Patrice Ossona De Mendez (CAMS), Xuding Zhu","submitted_at":"2011-08-08T07:32:16Z","abstract_excerpt":"The arboricity of a graph G is the minimum number of colours needed to colour the edges of G so that every cycle gets at least two colours. Given a positive integer p, we define the generalized p-arboricity Arb_p(G) of a graph G as the minimum number of colours needed to colour the edges of a multigraph G in such a way that every cycle C gets at least min(|C|; p + 1) colours. In the particular case where G has girth at least p + 1, Arb_p(G) is the minimum size of a partition of the edge set of G such that the union of any p parts induce a forest. If we require further that the edge colouring b"},"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":"1108.1616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-08T07:32:16Z","cross_cats_sorted":[],"title_canon_sha256":"09b29f9b5a4ed4459b48d50caaadab43c0ad30645864a76b6a3a31063a8ad9f4","abstract_canon_sha256":"98009ed62f2f0e8bee623a2acaabacd72c63ca6dc0bfb76ed3a723c3ce573bcb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:00.569925Z","signature_b64":"iiNLzWZ8FM03vmgt3vEMUddt9qycK0BLGnS3KdnfgaFRD8FwKKT0LAvKtcPTl+roWfZc1XqEy898faq2+L9pBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60b92ff60d1cf1e5f08ec4e67f2eae5cb930c686f29a2dafe45e9f42a01c613b","last_reissued_at":"2026-05-18T04:16:00.569193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:00.569193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Colouring Edges with many Colours in Cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jaroslav Nesetril (KAM), Patrice Ossona De Mendez (CAMS), Xuding Zhu","submitted_at":"2011-08-08T07:32:16Z","abstract_excerpt":"The arboricity of a graph G is the minimum number of colours needed to colour the edges of G so that every cycle gets at least two colours. Given a positive integer p, we define the generalized p-arboricity Arb_p(G) of a graph G as the minimum number of colours needed to colour the edges of a multigraph G in such a way that every cycle C gets at least min(|C|; p + 1) colours. In the particular case where G has girth at least p + 1, Arb_p(G) is the minimum size of a partition of the edge set of G such that the union of any p parts induce a forest. If we require further that the edge colouring b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1616","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":"1108.1616","created_at":"2026-05-18T04:16:00.569309+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.1616v1","created_at":"2026-05-18T04:16:00.569309+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.1616","created_at":"2026-05-18T04:16:00.569309+00:00"},{"alias_kind":"pith_short_12","alias_value":"MC4S75QNDTY6","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"MC4S75QNDTY6L4EO","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"MC4S75QN","created_at":"2026-05-18T12:26:34.985390+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/MC4S75QNDTY6L4EOYTTH6LVOLS","json":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS.json","graph_json":"https://pith.science/api/pith-number/MC4S75QNDTY6L4EOYTTH6LVOLS/graph.json","events_json":"https://pith.science/api/pith-number/MC4S75QNDTY6L4EOYTTH6LVOLS/events.json","paper":"https://pith.science/paper/MC4S75QN"},"agent_actions":{"view_html":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS","download_json":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS.json","view_paper":"https://pith.science/paper/MC4S75QN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.1616&json=true","fetch_graph":"https://pith.science/api/pith-number/MC4S75QNDTY6L4EOYTTH6LVOLS/graph.json","fetch_events":"https://pith.science/api/pith-number/MC4S75QNDTY6L4EOYTTH6LVOLS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS/action/storage_attestation","attest_author":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS/action/author_attestation","sign_citation":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS/action/citation_signature","submit_replication":"https://pith.science/pith/MC4S75QNDTY6L4EOYTTH6LVOLS/action/replication_record"}},"created_at":"2026-05-18T04:16:00.569309+00:00","updated_at":"2026-05-18T04:16:00.569309+00:00"}