{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:25MT7X52URNWEVP3QALGS43J2F","short_pith_number":"pith:25MT7X52","schema_version":"1.0","canonical_sha256":"d7593fdfbaa45b6255fb8016697369d14cbcd94ff9061b724874d4597ccdbf31","source":{"kind":"arxiv","id":"1406.4056","version":1},"attestation_state":"computed","paper":{"title":"Counting perfect matchings in graphs that exclude a single-crossing minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Radu Curticapean","submitted_at":"2014-06-16T16:06:46Z","abstract_excerpt":"A graph $H$ is single-crossing if it can be drawn in the plane with at most one crossing. For any single-crossing graph $H$, we give an $O(n^4)$ time algorithm for counting perfect matchings in graphs excluding $H$ as a minor. The runtime can be lowered to $O(n^{1.5})$ when $G$ excludes $K_5$ or $K_{3,3}$ as a minor. This is the first generalization of an algorithm for counting perfect matchings in $K_{3,3}$-free graphs (Little 1974, Vazirani 1989). Our algorithm uses black-boxes for counting perfect matchings in planar graphs and for computing certain graph decompositions. Together with an in"},"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":"1406.4056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-06-16T16:06:46Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"62fe11419a7e762e3a129409f7e69ae76430469596ddea3648903b8e59c583fd","abstract_canon_sha256":"884c928909cb1f3ec4a72943884de57731fca0ca177c3531bce13ee2c7eb7212"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:39.305343Z","signature_b64":"xyBsyzWMRfpRjs2bvPMwXVa21eHkKhvXxc3ju5nboNHmH11M0/ZcgQgJZKGIdHdm2kbgsnDPhCK+i0/pAwLWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7593fdfbaa45b6255fb8016697369d14cbcd94ff9061b724874d4597ccdbf31","last_reissued_at":"2026-05-18T02:49:39.305016Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:39.305016Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting perfect matchings in graphs that exclude a single-crossing minor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DS","authors_text":"Radu Curticapean","submitted_at":"2014-06-16T16:06:46Z","abstract_excerpt":"A graph $H$ is single-crossing if it can be drawn in the plane with at most one crossing. For any single-crossing graph $H$, we give an $O(n^4)$ time algorithm for counting perfect matchings in graphs excluding $H$ as a minor. The runtime can be lowered to $O(n^{1.5})$ when $G$ excludes $K_5$ or $K_{3,3}$ as a minor. This is the first generalization of an algorithm for counting perfect matchings in $K_{3,3}$-free graphs (Little 1974, Vazirani 1989). Our algorithm uses black-boxes for counting perfect matchings in planar graphs and for computing certain graph decompositions. Together with an in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4056","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":"1406.4056","created_at":"2026-05-18T02:49:39.305064+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.4056v1","created_at":"2026-05-18T02:49:39.305064+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4056","created_at":"2026-05-18T02:49:39.305064+00:00"},{"alias_kind":"pith_short_12","alias_value":"25MT7X52URNW","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"25MT7X52URNWEVP3","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"25MT7X52","created_at":"2026-05-18T12:28:09.283467+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/25MT7X52URNWEVP3QALGS43J2F","json":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F.json","graph_json":"https://pith.science/api/pith-number/25MT7X52URNWEVP3QALGS43J2F/graph.json","events_json":"https://pith.science/api/pith-number/25MT7X52URNWEVP3QALGS43J2F/events.json","paper":"https://pith.science/paper/25MT7X52"},"agent_actions":{"view_html":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F","download_json":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F.json","view_paper":"https://pith.science/paper/25MT7X52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.4056&json=true","fetch_graph":"https://pith.science/api/pith-number/25MT7X52URNWEVP3QALGS43J2F/graph.json","fetch_events":"https://pith.science/api/pith-number/25MT7X52URNWEVP3QALGS43J2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F/action/storage_attestation","attest_author":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F/action/author_attestation","sign_citation":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F/action/citation_signature","submit_replication":"https://pith.science/pith/25MT7X52URNWEVP3QALGS43J2F/action/replication_record"}},"created_at":"2026-05-18T02:49:39.305064+00:00","updated_at":"2026-05-18T02:49:39.305064+00:00"}