{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:7QTCAJIKGM7QZEZGYGO6ZKWDVC","short_pith_number":"pith:7QTCAJIK","schema_version":"1.0","canonical_sha256":"fc2620250a333f0c9326c19decaac3a8aa5fabf47e30feacadcaa032182471e7","source":{"kind":"arxiv","id":"1108.2521","version":1},"attestation_state":"computed","paper":{"title":"Rainbow Matchings of size \\delta(G) in Properly Edge-colored Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Casey Moffatt, Florian Pfender, Jennifer Diemunsch, Michael Ferrara, Paul S. Wenger","submitted_at":"2011-08-11T21:10:57Z","abstract_excerpt":"A {\\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(\\delta) such that a properly edge-colored graph G with minimum degree \\delta and order at least f(\\delta) must have a rainbow matching of size \\delta. We answer this question in the affirmative; f(\\delta) = 6.5\\delta suffices. Furthermore, the proof provides a O(\\delta(G)|V(G)|^2)-time algorithm that generates such a matching."},"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":"1108.2521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-11T21:10:57Z","cross_cats_sorted":[],"title_canon_sha256":"a0b8ecb1d5279172577f102eca6b574035a80d12bb4917ef4d2536f5129969da","abstract_canon_sha256":"396c8aa0ded7945525c6cd232c0256edfbe1ee067031fa523b325c3a82e1d508"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:36.587175Z","signature_b64":"d+LYY7JFks0aJkfSvWG1x2wCEnI9SUkisGa/jy3IGp4Njwd6unyivPnyekAT0mg82GTHp0/8QTxr443gdIlLAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc2620250a333f0c9326c19decaac3a8aa5fabf47e30feacadcaa032182471e7","last_reissued_at":"2026-05-18T04:15:36.586793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:36.586793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rainbow Matchings of size \\delta(G) in Properly Edge-colored Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Casey Moffatt, Florian Pfender, Jennifer Diemunsch, Michael Ferrara, Paul S. Wenger","submitted_at":"2011-08-11T21:10:57Z","abstract_excerpt":"A {\\it rainbow matching} in an edge-colored graph is a matching in which all the edges have distinct colors. Wang asked if there is a function f(\\delta) such that a properly edge-colored graph G with minimum degree \\delta and order at least f(\\delta) must have a rainbow matching of size \\delta. We answer this question in the affirmative; f(\\delta) = 6.5\\delta suffices. Furthermore, the proof provides a O(\\delta(G)|V(G)|^2)-time algorithm that generates such a matching."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2521","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":"1108.2521","created_at":"2026-05-18T04:15:36.586853+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.2521v1","created_at":"2026-05-18T04:15:36.586853+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.2521","created_at":"2026-05-18T04:15:36.586853+00:00"},{"alias_kind":"pith_short_12","alias_value":"7QTCAJIKGM7Q","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_16","alias_value":"7QTCAJIKGM7QZEZG","created_at":"2026-05-18T12:26:22.705136+00:00"},{"alias_kind":"pith_short_8","alias_value":"7QTCAJIK","created_at":"2026-05-18T12:26:22.705136+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/7QTCAJIKGM7QZEZGYGO6ZKWDVC","json":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC.json","graph_json":"https://pith.science/api/pith-number/7QTCAJIKGM7QZEZGYGO6ZKWDVC/graph.json","events_json":"https://pith.science/api/pith-number/7QTCAJIKGM7QZEZGYGO6ZKWDVC/events.json","paper":"https://pith.science/paper/7QTCAJIK"},"agent_actions":{"view_html":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC","download_json":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC.json","view_paper":"https://pith.science/paper/7QTCAJIK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.2521&json=true","fetch_graph":"https://pith.science/api/pith-number/7QTCAJIKGM7QZEZGYGO6ZKWDVC/graph.json","fetch_events":"https://pith.science/api/pith-number/7QTCAJIKGM7QZEZGYGO6ZKWDVC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC/action/storage_attestation","attest_author":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC/action/author_attestation","sign_citation":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC/action/citation_signature","submit_replication":"https://pith.science/pith/7QTCAJIKGM7QZEZGYGO6ZKWDVC/action/replication_record"}},"created_at":"2026-05-18T04:15:36.586853+00:00","updated_at":"2026-05-18T04:15:36.586853+00:00"}