{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:B7QVFNBBPR34AU462KBMN357L6","short_pith_number":"pith:B7QVFNBB","schema_version":"1.0","canonical_sha256":"0fe152b4217c77c0539ed282c6efbf5f84f5028d775aec0ea4b11a212710d62a","source":{"kind":"arxiv","id":"1204.3193","version":1},"attestation_state":"computed","paper":{"title":"Large rainbow matchings in large graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Florian Pfender, Matthew Yancey","submitted_at":"2012-04-14T18:14:32Z","abstract_excerpt":"A \\textit{rainbow subgraph} of an edge-colored graph is a subgraph whose edges have distinct colors. The \\textit{color degree} of a vertex $v$ is the number of different colors on edges incident to $v$. We show that if $n$ is large enough (namely, $n\\geq 4.25k^2$), then each $n$-vertex graph $G$ with minimum color degree at least $k$ contains a rainbow matching of size at least $k$."},"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":"1204.3193","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-14T18:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"0d70c0de6c51151fe2eea42957516deca0d5a3f80823b859fdf418f90af28eb6","abstract_canon_sha256":"e084a2895d098f987fe39df7d4d361fb8296a4964cad291d09012771fd4e7404"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:52.305440Z","signature_b64":"KTMocno6nrN6PK9VZQKZghUTtQPEozzXNmDmK4ZvJAqgR2e3f/8CmImmoUHSBK2RLyvDW1vAXorVJjSL8bGFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fe152b4217c77c0539ed282c6efbf5f84f5028d775aec0ea4b11a212710d62a","last_reissued_at":"2026-05-18T03:57:52.304844Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:52.304844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large rainbow matchings in large graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandr Kostochka, Florian Pfender, Matthew Yancey","submitted_at":"2012-04-14T18:14:32Z","abstract_excerpt":"A \\textit{rainbow subgraph} of an edge-colored graph is a subgraph whose edges have distinct colors. The \\textit{color degree} of a vertex $v$ is the number of different colors on edges incident to $v$. We show that if $n$ is large enough (namely, $n\\geq 4.25k^2$), then each $n$-vertex graph $G$ with minimum color degree at least $k$ contains a rainbow matching of size at least $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3193","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":"1204.3193","created_at":"2026-05-18T03:57:52.304943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.3193v1","created_at":"2026-05-18T03:57:52.304943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3193","created_at":"2026-05-18T03:57:52.304943+00:00"},{"alias_kind":"pith_short_12","alias_value":"B7QVFNBBPR34","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"B7QVFNBBPR34AU46","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"B7QVFNBB","created_at":"2026-05-18T12:26:58.693483+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/B7QVFNBBPR34AU462KBMN357L6","json":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6.json","graph_json":"https://pith.science/api/pith-number/B7QVFNBBPR34AU462KBMN357L6/graph.json","events_json":"https://pith.science/api/pith-number/B7QVFNBBPR34AU462KBMN357L6/events.json","paper":"https://pith.science/paper/B7QVFNBB"},"agent_actions":{"view_html":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6","download_json":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6.json","view_paper":"https://pith.science/paper/B7QVFNBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.3193&json=true","fetch_graph":"https://pith.science/api/pith-number/B7QVFNBBPR34AU462KBMN357L6/graph.json","fetch_events":"https://pith.science/api/pith-number/B7QVFNBBPR34AU462KBMN357L6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6/action/storage_attestation","attest_author":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6/action/author_attestation","sign_citation":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6/action/citation_signature","submit_replication":"https://pith.science/pith/B7QVFNBBPR34AU462KBMN357L6/action/replication_record"}},"created_at":"2026-05-18T03:57:52.304943+00:00","updated_at":"2026-05-18T03:57:52.304943+00:00"}