{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:3ES75LUY62LPPXQDVJHCYP25YF","short_pith_number":"pith:3ES75LUY","schema_version":"1.0","canonical_sha256":"d925feae98f696f7de03aa4e2c3f5dc179b645a4d0eec76257b5208a0d95c803","source":{"kind":"arxiv","id":"0910.0079","version":1},"attestation_state":"computed","paper":{"title":"Rank-width and Tree-width of H-minor-free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dimitrios M. Thilikos, Fedor V. Fomin, Sang-il Oum","submitted_at":"2009-10-01T05:00:25Z","abstract_excerpt":"We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as K_r-minor free graphs and graphs of bounded genus."},"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":"0910.0079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-10-01T05:00:25Z","cross_cats_sorted":[],"title_canon_sha256":"81bab6bdef3532886f882dc9740f05ce46ccace98552b1501a201caeb9db4ec2","abstract_canon_sha256":"600ff78125886646a2179f3d4f1c6f9c5d88649ff2cf64ae4f24df15dff8dcab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:39.696730Z","signature_b64":"yvwSPT92fw1+NDTla/bZWp/7hUJkX4SVZSd0byF3NPmpdQnL9ZJpRcYvqHnaYAXi/Qa9gxoUAGM4gtCwQd8zBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d925feae98f696f7de03aa4e2c3f5dc179b645a4d0eec76257b5208a0d95c803","last_reissued_at":"2026-05-18T02:55:39.696065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:39.696065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rank-width and Tree-width of H-minor-free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dimitrios M. Thilikos, Fedor V. Fomin, Sang-il Oum","submitted_at":"2009-10-01T05:00:25Z","abstract_excerpt":"We prove that for any fixed r>=2, the tree-width of graphs not containing K_r as a topological minor (resp. as a subgraph) is bounded by a linear (resp. polynomial) function of their rank-width. We also present refinements of our bounds for other graph classes such as K_r-minor free graphs and graphs of bounded genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.0079","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":"0910.0079","created_at":"2026-05-18T02:55:39.696183+00:00"},{"alias_kind":"arxiv_version","alias_value":"0910.0079v1","created_at":"2026-05-18T02:55:39.696183+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.0079","created_at":"2026-05-18T02:55:39.696183+00:00"},{"alias_kind":"pith_short_12","alias_value":"3ES75LUY62LP","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"3ES75LUY62LPPXQD","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"3ES75LUY","created_at":"2026-05-18T12:25:58.018023+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/3ES75LUY62LPPXQDVJHCYP25YF","json":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF.json","graph_json":"https://pith.science/api/pith-number/3ES75LUY62LPPXQDVJHCYP25YF/graph.json","events_json":"https://pith.science/api/pith-number/3ES75LUY62LPPXQDVJHCYP25YF/events.json","paper":"https://pith.science/paper/3ES75LUY"},"agent_actions":{"view_html":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF","download_json":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF.json","view_paper":"https://pith.science/paper/3ES75LUY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0910.0079&json=true","fetch_graph":"https://pith.science/api/pith-number/3ES75LUY62LPPXQDVJHCYP25YF/graph.json","fetch_events":"https://pith.science/api/pith-number/3ES75LUY62LPPXQDVJHCYP25YF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF/action/storage_attestation","attest_author":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF/action/author_attestation","sign_citation":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF/action/citation_signature","submit_replication":"https://pith.science/pith/3ES75LUY62LPPXQDVJHCYP25YF/action/replication_record"}},"created_at":"2026-05-18T02:55:39.696183+00:00","updated_at":"2026-05-18T02:55:39.696183+00:00"}