{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3QJA47CL6PRFHBLZNZDQBS6QGV","short_pith_number":"pith:3QJA47CL","schema_version":"1.0","canonical_sha256":"dc120e7c4bf3e25385796e4700cbd0356b7e352993eb477dc56f51785e89779e","source":{"kind":"arxiv","id":"1509.00569","version":1},"attestation_state":"computed","paper":{"title":"The maximum number of perfect matchings of semi-regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G.L. Wang, Hongliang Lu","submitted_at":"2015-09-02T06:29:33Z","abstract_excerpt":"Let $n\\ge 34$ be an even integer, and $D_n=2\\lceil n/4 \\rceil-1$. In this paper, we prove that every $\\{D_n,\\,D_n+1\\}$-graph of order $n$ contains $\\lceil n/4 \\rceil$ disjoint perfect matchings. This result is sharp in the sense that (i) there exists a $\\{D_n,\\,D_n+1\\}$-graph containing exactly $\\lceil n/4 \\rceil$ disjoint perfect matchings, and that (ii) there exists a $\\{D_n-1,\\,D_n\\}$-graph without perfect matchings for each $n$. As a consequence, for any integer $D\\ge D_n$, every $\\{D,\\,D+1\\}$-graph of order $n$ contains $\\lceil (D+1)/2 \\rceil$ disjoint perfect matchings. This extends Csab"},"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":"1509.00569","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-09-02T06:29:33Z","cross_cats_sorted":[],"title_canon_sha256":"02f77237d839d075f70264f7dbfd673880394fcd8113cbd125fee8ae60a3171c","abstract_canon_sha256":"18d85672e9ac0d113943c6e7896d561e287903cc82c9dcf0e9c1b9c33a14bdf9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:06.805691Z","signature_b64":"KBrC3N7ZlY039V3x0LMtBJ/UA2t/u7lWXo7grbN9NCCMN9zty73C/RgUaO/BKvnahvU+n+EKL4kFYuw/bIW2DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc120e7c4bf3e25385796e4700cbd0356b7e352993eb477dc56f51785e89779e","last_reissued_at":"2026-05-18T01:34:06.805143Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:06.805143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The maximum number of perfect matchings of semi-regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"David G.L. Wang, Hongliang Lu","submitted_at":"2015-09-02T06:29:33Z","abstract_excerpt":"Let $n\\ge 34$ be an even integer, and $D_n=2\\lceil n/4 \\rceil-1$. In this paper, we prove that every $\\{D_n,\\,D_n+1\\}$-graph of order $n$ contains $\\lceil n/4 \\rceil$ disjoint perfect matchings. This result is sharp in the sense that (i) there exists a $\\{D_n,\\,D_n+1\\}$-graph containing exactly $\\lceil n/4 \\rceil$ disjoint perfect matchings, and that (ii) there exists a $\\{D_n-1,\\,D_n\\}$-graph without perfect matchings for each $n$. As a consequence, for any integer $D\\ge D_n$, every $\\{D,\\,D+1\\}$-graph of order $n$ contains $\\lceil (D+1)/2 \\rceil$ disjoint perfect matchings. This extends Csab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00569","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":"1509.00569","created_at":"2026-05-18T01:34:06.805223+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.00569v1","created_at":"2026-05-18T01:34:06.805223+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00569","created_at":"2026-05-18T01:34:06.805223+00:00"},{"alias_kind":"pith_short_12","alias_value":"3QJA47CL6PRF","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3QJA47CL6PRFHBLZ","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3QJA47CL","created_at":"2026-05-18T12:29:02.477457+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/3QJA47CL6PRFHBLZNZDQBS6QGV","json":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV.json","graph_json":"https://pith.science/api/pith-number/3QJA47CL6PRFHBLZNZDQBS6QGV/graph.json","events_json":"https://pith.science/api/pith-number/3QJA47CL6PRFHBLZNZDQBS6QGV/events.json","paper":"https://pith.science/paper/3QJA47CL"},"agent_actions":{"view_html":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV","download_json":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV.json","view_paper":"https://pith.science/paper/3QJA47CL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.00569&json=true","fetch_graph":"https://pith.science/api/pith-number/3QJA47CL6PRFHBLZNZDQBS6QGV/graph.json","fetch_events":"https://pith.science/api/pith-number/3QJA47CL6PRFHBLZNZDQBS6QGV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV/action/storage_attestation","attest_author":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV/action/author_attestation","sign_citation":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV/action/citation_signature","submit_replication":"https://pith.science/pith/3QJA47CL6PRFHBLZNZDQBS6QGV/action/replication_record"}},"created_at":"2026-05-18T01:34:06.805223+00:00","updated_at":"2026-05-18T01:34:06.805223+00:00"}