{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:GNO74W2B2HT7LWYF4SMYU74ZQU","short_pith_number":"pith:GNO74W2B","schema_version":"1.0","canonical_sha256":"335dfe5b41d1e7f5db05e4998a7f998518d166d0e9e99dd582828a24a7400c44","source":{"kind":"arxiv","id":"1204.2727","version":5},"attestation_state":"computed","paper":{"title":"The Cost of Perfection for Matchings in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Celina de Figueiredo, Diana Sasaki, Emilio Vital Brazil, Guilherme D. da Fonseca","submitted_at":"2012-04-11T17:51:22Z","abstract_excerpt":"Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs. First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses o"},"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":"1204.2727","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-04-11T17:51:22Z","cross_cats_sorted":[],"title_canon_sha256":"a24447816e40a71209e637ac8dff70563683ae6beaac570f43432681bd5131c2","abstract_canon_sha256":"beba6f3fc4350db0b9c0517ff310b90bd581bbda8c4ed84e1bd3c93faa34afd9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:23.880586Z","signature_b64":"/TYKTE/T6E46Q87XOwcQob3B9TTAf6DgKzbz4Ul+PKi2zQwfOcMhgYkDHqE6KUteR+FJ/N9vU1gvHjJ1drmzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"335dfe5b41d1e7f5db05e4998a7f998518d166d0e9e99dd582828a24a7400c44","last_reissued_at":"2026-05-18T00:01:23.880174Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:23.880174Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Cost of Perfection for Matchings in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Celina de Figueiredo, Diana Sasaki, Emilio Vital Brazil, Guilherme D. da Fonseca","submitted_at":"2012-04-11T17:51:22Z","abstract_excerpt":"Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer graphics application in triangle meshes, where we seek to convert a triangulation into a quadrangulation by merging pairs of adjacent triangles, we focus mainly on bridgeless cubic graphs. First, we characterize graphs that attain the extreme ratios. Second, we present a lower bound for all bridgeless cubic graphs. Third, we present upper bounds for subclasses o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2727","kind":"arxiv","version":5},"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":"1204.2727","created_at":"2026-05-18T00:01:23.880231+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.2727v5","created_at":"2026-05-18T00:01:23.880231+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2727","created_at":"2026-05-18T00:01:23.880231+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNO74W2B2HT7","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNO74W2B2HT7LWYF","created_at":"2026-05-18T12:27:06.952714+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNO74W2B","created_at":"2026-05-18T12:27:06.952714+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/GNO74W2B2HT7LWYF4SMYU74ZQU","json":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU.json","graph_json":"https://pith.science/api/pith-number/GNO74W2B2HT7LWYF4SMYU74ZQU/graph.json","events_json":"https://pith.science/api/pith-number/GNO74W2B2HT7LWYF4SMYU74ZQU/events.json","paper":"https://pith.science/paper/GNO74W2B"},"agent_actions":{"view_html":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU","download_json":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU.json","view_paper":"https://pith.science/paper/GNO74W2B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.2727&json=true","fetch_graph":"https://pith.science/api/pith-number/GNO74W2B2HT7LWYF4SMYU74ZQU/graph.json","fetch_events":"https://pith.science/api/pith-number/GNO74W2B2HT7LWYF4SMYU74ZQU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU/action/storage_attestation","attest_author":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU/action/author_attestation","sign_citation":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU/action/citation_signature","submit_replication":"https://pith.science/pith/GNO74W2B2HT7LWYF4SMYU74ZQU/action/replication_record"}},"created_at":"2026-05-18T00:01:23.880231+00:00","updated_at":"2026-05-18T00:01:23.880231+00:00"}