{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3A35LMRVIBPPCODJES32T64HH6","short_pith_number":"pith:3A35LMRV","schema_version":"1.0","canonical_sha256":"d837d5b235405ef1386924b7a9fb873fbbabe0bcbf1850f62a46b8f13759296b","source":{"kind":"arxiv","id":"1401.8023","version":1},"attestation_state":"computed","paper":{"title":"Brooks' Vertex-Colouring Theorem in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bradley Baetz, David R. Wood","submitted_at":"2014-01-30T23:11:08Z","abstract_excerpt":"Brooks' Theorem [R. L. Brooks, On Colouring the Nodes of a Network, Proc. Cambridge Philos. Soc.} 37:194-197, 1941] states that every graph $G$ with maximum degree $\\Delta$, has a vertex-colouring with $\\Delta$ colours, unless $G$ is a complete graph or an odd cycle, in which case $\\Delta+1$ colours are required. Lov\\'asz [L. Lov\\'asz, Three short proofs in graph theory, J. Combin. Theory Ser. 19:269-271, 1975] gives an algorithmic proof of Brooks' Theorem. Unfortunately this proof is missing important details and it is thus unclear whether it leads to a linear time algorithm. In this paper we"},"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":"1401.8023","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-01-30T23:11:08Z","cross_cats_sorted":[],"title_canon_sha256":"f11ba13eafc93a3bbf055ac634e976359c30ccb046a2e37c7bbecd8529df5d71","abstract_canon_sha256":"8a52afd854b8ca3dcee300e15010e91e392431acf966ab7a9a533e1cac66fb42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:36.452809Z","signature_b64":"fWR0hNvwN+cQu6RxqhyZOiH6wjK2T93k2RkthrMEsqexD8Abk3yUVBPvlBIpywPmmjm04O2i1mO2ytpu6+X1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d837d5b235405ef1386924b7a9fb873fbbabe0bcbf1850f62a46b8f13759296b","last_reissued_at":"2026-05-18T03:00:36.451943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:36.451943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Brooks' Vertex-Colouring Theorem in Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bradley Baetz, David R. Wood","submitted_at":"2014-01-30T23:11:08Z","abstract_excerpt":"Brooks' Theorem [R. L. Brooks, On Colouring the Nodes of a Network, Proc. Cambridge Philos. Soc.} 37:194-197, 1941] states that every graph $G$ with maximum degree $\\Delta$, has a vertex-colouring with $\\Delta$ colours, unless $G$ is a complete graph or an odd cycle, in which case $\\Delta+1$ colours are required. Lov\\'asz [L. Lov\\'asz, Three short proofs in graph theory, J. Combin. Theory Ser. 19:269-271, 1975] gives an algorithmic proof of Brooks' Theorem. Unfortunately this proof is missing important details and it is thus unclear whether it leads to a linear time algorithm. In this paper we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8023","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":"1401.8023","created_at":"2026-05-18T03:00:36.452103+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.8023v1","created_at":"2026-05-18T03:00:36.452103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.8023","created_at":"2026-05-18T03:00:36.452103+00:00"},{"alias_kind":"pith_short_12","alias_value":"3A35LMRVIBPP","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3A35LMRVIBPPCODJ","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3A35LMRV","created_at":"2026-05-18T12:28:11.866339+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.03735","citing_title":"Approximation Algorithms for Matroid-Intersection Coloring with Applications to Rota's Basis Conjecture","ref_index":4,"is_internal_anchor":false},{"citing_arxiv_id":"2605.07774","citing_title":"Beyond Brooks: $(\\Delta-1)$-Coloring in Semi-Streaming","ref_index":46,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6","json":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6.json","graph_json":"https://pith.science/api/pith-number/3A35LMRVIBPPCODJES32T64HH6/graph.json","events_json":"https://pith.science/api/pith-number/3A35LMRVIBPPCODJES32T64HH6/events.json","paper":"https://pith.science/paper/3A35LMRV"},"agent_actions":{"view_html":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6","download_json":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6.json","view_paper":"https://pith.science/paper/3A35LMRV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.8023&json=true","fetch_graph":"https://pith.science/api/pith-number/3A35LMRVIBPPCODJES32T64HH6/graph.json","fetch_events":"https://pith.science/api/pith-number/3A35LMRVIBPPCODJES32T64HH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6/action/storage_attestation","attest_author":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6/action/author_attestation","sign_citation":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6/action/citation_signature","submit_replication":"https://pith.science/pith/3A35LMRVIBPPCODJES32T64HH6/action/replication_record"}},"created_at":"2026-05-18T03:00:36.452103+00:00","updated_at":"2026-05-18T03:00:36.452103+00:00"}