{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:FREV6Y43CQAJMVKFHVWOKXUIJ6","short_pith_number":"pith:FREV6Y43","schema_version":"1.0","canonical_sha256":"2c495f639b14009655453d6ce55e884fb42bbaddd69e1e56b3649f277924e8ce","source":{"kind":"arxiv","id":"1603.05018","version":3},"attestation_state":"computed","paper":{"title":"Chromatic index, treewidth and maximum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henning Bruhn, Laura Gellert, Richard Lang","submitted_at":"2016-03-16T10:26:02Z","abstract_excerpt":"We conjecture that any graph $G$ with treewidth~$k$ and maximum degree $\\Delta(G)\\geq k + \\sqrt{k}$ satisfies $\\chi'(G)=\\Delta(G)$. In support of the conjecture we prove its fractional version. We also show that any graph $G$ with treewidth~$k\\geq 4$ and maximum degree $2k-1$ satisfies $\\chi'(G)=\\Delta(G)$, improving an old result of Vizing."},"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":"1603.05018","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-16T10:26:02Z","cross_cats_sorted":[],"title_canon_sha256":"249eff09c2e737a039a27b95e6d5b6959181b3b93c261fda80eef69cf286c82b","abstract_canon_sha256":"3fa39ab9d85cac0b6ac2879f4a3aeeb8538682224ac56d27d215d5c6f5efc795"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:46.529232Z","signature_b64":"GCsTKDF65EJRi/esLEceba54NBDO/mJQsVVaiDtpnROLzja6KUr2UNFTczmhBQIqzjg9y/HEvuP2vYFaKVFMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c495f639b14009655453d6ce55e884fb42bbaddd69e1e56b3649f277924e8ce","last_reissued_at":"2026-05-18T00:17:46.528598Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:46.528598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chromatic index, treewidth and maximum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Henning Bruhn, Laura Gellert, Richard Lang","submitted_at":"2016-03-16T10:26:02Z","abstract_excerpt":"We conjecture that any graph $G$ with treewidth~$k$ and maximum degree $\\Delta(G)\\geq k + \\sqrt{k}$ satisfies $\\chi'(G)=\\Delta(G)$. In support of the conjecture we prove its fractional version. We also show that any graph $G$ with treewidth~$k\\geq 4$ and maximum degree $2k-1$ satisfies $\\chi'(G)=\\Delta(G)$, improving an old result of Vizing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05018","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1603.05018","created_at":"2026-05-18T00:17:46.528694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.05018v3","created_at":"2026-05-18T00:17:46.528694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05018","created_at":"2026-05-18T00:17:46.528694+00:00"},{"alias_kind":"pith_short_12","alias_value":"FREV6Y43CQAJ","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_16","alias_value":"FREV6Y43CQAJMVKF","created_at":"2026-05-18T12:30:15.759754+00:00"},{"alias_kind":"pith_short_8","alias_value":"FREV6Y43","created_at":"2026-05-18T12:30:15.759754+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/FREV6Y43CQAJMVKFHVWOKXUIJ6","json":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6.json","graph_json":"https://pith.science/api/pith-number/FREV6Y43CQAJMVKFHVWOKXUIJ6/graph.json","events_json":"https://pith.science/api/pith-number/FREV6Y43CQAJMVKFHVWOKXUIJ6/events.json","paper":"https://pith.science/paper/FREV6Y43"},"agent_actions":{"view_html":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6","download_json":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6.json","view_paper":"https://pith.science/paper/FREV6Y43","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.05018&json=true","fetch_graph":"https://pith.science/api/pith-number/FREV6Y43CQAJMVKFHVWOKXUIJ6/graph.json","fetch_events":"https://pith.science/api/pith-number/FREV6Y43CQAJMVKFHVWOKXUIJ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6/action/storage_attestation","attest_author":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6/action/author_attestation","sign_citation":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6/action/citation_signature","submit_replication":"https://pith.science/pith/FREV6Y43CQAJMVKFHVWOKXUIJ6/action/replication_record"}},"created_at":"2026-05-18T00:17:46.528694+00:00","updated_at":"2026-05-18T00:17:46.528694+00:00"}