{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VDOHJGNOM2YBRP5YIN7JD6XW6Q","short_pith_number":"pith:VDOHJGNO","schema_version":"1.0","canonical_sha256":"a8dc7499ae66b018bfb8437e91faf6f40d528168c1965d890e735dee0fe01598","source":{"kind":"arxiv","id":"1311.0573","version":3},"attestation_state":"computed","paper":{"title":"Graphs with no 7-wheel subdivision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Graham Farr, Rebecca Robinson","submitted_at":"2013-11-04T03:19:39Z","abstract_excerpt":"The subgraph homeomorphism problem, SHP($H$), has been shown to be polynomial-time solvable for any fixed pattern graph $H$, but practical algorithms have been developed only for a few specific pattern graphs. Among these are the wheels with four, five, and six spokes. This paper examines the subgraph homeomorphism problem where the pattern graph is a wheel with seven spokes, and gives a result that describes graphs with no $W_{7}$-subdivision, showing how they can be built up, using certain operations, from smaller `pieces' that meet certain conditions. We also discuss algorithmic aspects of "},"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":"1311.0573","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-11-04T03:19:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fe3df1d23ee2ff32b070660136f734cf6d2fef7e044afb66c25560087a24604d","abstract_canon_sha256":"90632927d1eafcfabb5a1ef815e1a93cba9856a6b2b55fb5657162ef5a7bbb3b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:04.996546Z","signature_b64":"wYCaesx7DhMXzIzrm4qVHCnM8CoMy4bIvzkxHjx1g3GU5Ub6u6z0ZaYOSZ56tGQNtch/txqxZHQpzNGgUKMlAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8dc7499ae66b018bfb8437e91faf6f40d528168c1965d890e735dee0fe01598","last_reissued_at":"2026-05-18T00:45:04.996138Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:04.996138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Graphs with no 7-wheel subdivision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Graham Farr, Rebecca Robinson","submitted_at":"2013-11-04T03:19:39Z","abstract_excerpt":"The subgraph homeomorphism problem, SHP($H$), has been shown to be polynomial-time solvable for any fixed pattern graph $H$, but practical algorithms have been developed only for a few specific pattern graphs. Among these are the wheels with four, five, and six spokes. This paper examines the subgraph homeomorphism problem where the pattern graph is a wheel with seven spokes, and gives a result that describes graphs with no $W_{7}$-subdivision, showing how they can be built up, using certain operations, from smaller `pieces' that meet certain conditions. We also discuss algorithmic aspects of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0573","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":"1311.0573","created_at":"2026-05-18T00:45:04.996198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.0573v3","created_at":"2026-05-18T00:45:04.996198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0573","created_at":"2026-05-18T00:45:04.996198+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDOHJGNOM2YB","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDOHJGNOM2YBRP5Y","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDOHJGNO","created_at":"2026-05-18T12:28:04.890932+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/VDOHJGNOM2YBRP5YIN7JD6XW6Q","json":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q.json","graph_json":"https://pith.science/api/pith-number/VDOHJGNOM2YBRP5YIN7JD6XW6Q/graph.json","events_json":"https://pith.science/api/pith-number/VDOHJGNOM2YBRP5YIN7JD6XW6Q/events.json","paper":"https://pith.science/paper/VDOHJGNO"},"agent_actions":{"view_html":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q","download_json":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q.json","view_paper":"https://pith.science/paper/VDOHJGNO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.0573&json=true","fetch_graph":"https://pith.science/api/pith-number/VDOHJGNOM2YBRP5YIN7JD6XW6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/VDOHJGNOM2YBRP5YIN7JD6XW6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q/action/storage_attestation","attest_author":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q/action/author_attestation","sign_citation":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q/action/citation_signature","submit_replication":"https://pith.science/pith/VDOHJGNOM2YBRP5YIN7JD6XW6Q/action/replication_record"}},"created_at":"2026-05-18T00:45:04.996198+00:00","updated_at":"2026-05-18T00:45:04.996198+00:00"}