{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:LPO4SGYDFLJOFHJOPOKS2566ZD","short_pith_number":"pith:LPO4SGYD","schema_version":"1.0","canonical_sha256":"5bddc91b032ad2e29d2e7b952d77dec8f7f23788051ae37e4416ec7ce302aa8f","source":{"kind":"arxiv","id":"1105.1764","version":1},"attestation_state":"computed","paper":{"title":"Generating p-extremal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Derrick Stolee","submitted_at":"2011-05-09T19:50:24Z","abstract_excerpt":"Define f(n,p) to be the maximum number of edges in a graph on n vertices with p perfect matchings. Dudek and Schmitt proved there exist constants n_p and c_p so that for even n >= n_p, f(n,p) = (n^2)/4+c_p. A graph is p-extremal if it has p perfect matchings and (n^2)/4+c_p edges. Based on Lovasz's Two Ear Theorem and structural results of Hartke, Stolee, West, and Yancey, we develop a computational method for determining c_p and generating the finite set of graphs which describe the infinite family of p-extremal graphs. This method extends the knowledge of the size and structure of p-extremal"},"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":"1105.1764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-09T19:50:24Z","cross_cats_sorted":[],"title_canon_sha256":"1debfe9152ae5e408599c76b94b59092533c4d23a46f53c6d3febb80c5865f30","abstract_canon_sha256":"f9f9653a9cc537489435ee005eb8b8a03669fcf1ff34bcb6244c321b86cebf0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:32.537201Z","signature_b64":"4KumhZZ9MCRJf6PSQhppFeBrrmkRr6Cv2DQ0JOff2U/AAMeObxMCnmG32Mt3I9Yp9Uw0XHnz/lOQrUFOB/VYDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5bddc91b032ad2e29d2e7b952d77dec8f7f23788051ae37e4416ec7ce302aa8f","last_reissued_at":"2026-05-18T04:22:32.536632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:32.536632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generating p-extremal graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Derrick Stolee","submitted_at":"2011-05-09T19:50:24Z","abstract_excerpt":"Define f(n,p) to be the maximum number of edges in a graph on n vertices with p perfect matchings. Dudek and Schmitt proved there exist constants n_p and c_p so that for even n >= n_p, f(n,p) = (n^2)/4+c_p. A graph is p-extremal if it has p perfect matchings and (n^2)/4+c_p edges. Based on Lovasz's Two Ear Theorem and structural results of Hartke, Stolee, West, and Yancey, we develop a computational method for determining c_p and generating the finite set of graphs which describe the infinite family of p-extremal graphs. This method extends the knowledge of the size and structure of p-extremal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1764","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":"1105.1764","created_at":"2026-05-18T04:22:32.536720+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.1764v1","created_at":"2026-05-18T04:22:32.536720+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1764","created_at":"2026-05-18T04:22:32.536720+00:00"},{"alias_kind":"pith_short_12","alias_value":"LPO4SGYDFLJO","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"LPO4SGYDFLJOFHJO","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"LPO4SGYD","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/LPO4SGYDFLJOFHJOPOKS2566ZD","json":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD.json","graph_json":"https://pith.science/api/pith-number/LPO4SGYDFLJOFHJOPOKS2566ZD/graph.json","events_json":"https://pith.science/api/pith-number/LPO4SGYDFLJOFHJOPOKS2566ZD/events.json","paper":"https://pith.science/paper/LPO4SGYD"},"agent_actions":{"view_html":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD","download_json":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD.json","view_paper":"https://pith.science/paper/LPO4SGYD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.1764&json=true","fetch_graph":"https://pith.science/api/pith-number/LPO4SGYDFLJOFHJOPOKS2566ZD/graph.json","fetch_events":"https://pith.science/api/pith-number/LPO4SGYDFLJOFHJOPOKS2566ZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD/action/storage_attestation","attest_author":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD/action/author_attestation","sign_citation":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD/action/citation_signature","submit_replication":"https://pith.science/pith/LPO4SGYDFLJOFHJOPOKS2566ZD/action/replication_record"}},"created_at":"2026-05-18T04:22:32.536720+00:00","updated_at":"2026-05-18T04:22:32.536720+00:00"}