{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QFWGH2RXNTERHBUQOLHW4Q6HDF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f7953f0adfb1bde661d4414cb4cf445292b635655e3af37f2b47525cef7da122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-28T14:05:43Z","title_canon_sha256":"235bc9b13f4c79d353de87e2ca219e5efc4e5b01dfddba09b4048877cbc747c2"},"schema_version":"1.0","source":{"id":"1208.5670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5670","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5670v1","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5670","created_at":"2026-05-18T03:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"QFWGH2RXNTER","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QFWGH2RXNTERHBUQ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QFWGH2RX","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:fdb7f9d5e62d44f9926d15450cb6cf6a68e6624f5dad64bf459df79ba9301a86","target":"graph","created_at":"2026-05-18T03:46:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we consider properly edge-colored graphs, i.e. two edges with the same color cannot share an endpoint, so each color class is a matching. A matching is called \\it rainbow \\rm if its edges have different colors. The minimum degree of a graph is denoted by $\\delta(G)$. We show that properly edge colored graphs $G$ with $|V(G)|\\ge 4\\delta(G)-3$ have rainbow matchings of size $\\delta(G)$, this gives the best known estimate to a recent question of Wang. Since one obviously needs at least $2\\delta(G)$ vertices to guarantee a rainbow matching of size $\\delta(G)$, we investigate what hap","authors_text":"Andras Gyarfas, Gabor N. Sarkozy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-28T14:05:43Z","title":"Rainbow matchings and partial transversals of Latin squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5670","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0d5f45e238110fce7b76dd1f21ee88aa8c77f42d326cde8dd1542560beee1ad2","target":"record","created_at":"2026-05-18T03:46:58Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f7953f0adfb1bde661d4414cb4cf445292b635655e3af37f2b47525cef7da122","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-08-28T14:05:43Z","title_canon_sha256":"235bc9b13f4c79d353de87e2ca219e5efc4e5b01dfddba09b4048877cbc747c2"},"schema_version":"1.0","source":{"id":"1208.5670","kind":"arxiv","version":1}},"canonical_sha256":"816c63ea376cc913869072cf6e43c7197a0b2b9df8db99a06ccc80398dc50244","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"816c63ea376cc913869072cf6e43c7197a0b2b9df8db99a06ccc80398dc50244","first_computed_at":"2026-05-18T03:46:58.088966Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:58.088966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hQrIptTFNBCfKQnYMBerYmwqh0EvBbRoMDPBP5lQFnkCQSyEm92dWPAKkWzpip/a81BmQowOsTEsFDKkPB7wAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:58.089704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d5f45e238110fce7b76dd1f21ee88aa8c77f42d326cde8dd1542560beee1ad2","sha256:fdb7f9d5e62d44f9926d15450cb6cf6a68e6624f5dad64bf459df79ba9301a86"],"state_sha256":"e434bd2ef326dadde8f2d6d58f6f832c43cdf8d0c8fb887e0c6e6cce19d4240a"}