{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GI5UUCQKM3O4FBN5CKVREFAF4C","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":"0c81e08af6a662479364e1731529e6152e81192a764b2f1450ffff796043bcca","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-09T11:43:15Z","title_canon_sha256":"e0880d40bb7b777344f13c42daf52bdc451b5a8e84c64856266ae4baf5698ccb"},"schema_version":"1.0","source":{"id":"1710.03041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03041","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03041v1","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03041","created_at":"2026-05-18T00:33:27Z"},{"alias_kind":"pith_short_12","alias_value":"GI5UUCQKM3O4","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GI5UUCQKM3O4FBN5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GI5UUCQK","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:0c4af90489adc44cb133742ce540e9edebf7bf2d4e04971a961574488c873e8e","target":"graph","created_at":"2026-05-18T00:33:27Z","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":"Aharoni and Berger conjectured that in any bipartite multigraph that is properly edge-coloured by $n$ colours with at least $n + 1$ edges of each colour there must be a matching that uses each colour exactly once. In this paper we consider the same question without the bipartiteness assumption. We show that in any multigraph with edge multiplicities $o(n)$ that is properly edge-coloured by $n$ colours with at least $n + o(n)$ edges of each colour there must be a matching of size $n-O(1)$ that uses each colour at most once.","authors_text":"Liana Yepremyan, Peter Keevash","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-09T11:43:15Z","title":"Rainbow matchings in properly-coloured multigraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03041","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":"sha256:83ab9b2e489cf29eac6d7f196dbb8c8caea6ce79509f202ac7baf8e542ab3ac3","target":"record","created_at":"2026-05-18T00:33:27Z","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":"0c81e08af6a662479364e1731529e6152e81192a764b2f1450ffff796043bcca","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-10-09T11:43:15Z","title_canon_sha256":"e0880d40bb7b777344f13c42daf52bdc451b5a8e84c64856266ae4baf5698ccb"},"schema_version":"1.0","source":{"id":"1710.03041","kind":"arxiv","version":1}},"canonical_sha256":"323b4a0a0a66ddc285bd12ab121405e0bb81b87e473d447df9683b2f983858ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"323b4a0a0a66ddc285bd12ab121405e0bb81b87e473d447df9683b2f983858ce","first_computed_at":"2026-05-18T00:33:27.219844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:27.219844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V8vYmq4ii5xcaE1k1EfYcmwLQ9JDfxJo11cC3jtGRKTefeXCKrb3lIxS67lLim485tokj+DJE6UuLOJFpaXVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:27.220490Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83ab9b2e489cf29eac6d7f196dbb8c8caea6ce79509f202ac7baf8e542ab3ac3","sha256:0c4af90489adc44cb133742ce540e9edebf7bf2d4e04971a961574488c873e8e"],"state_sha256":"2bc29a50aa5ff6fe5ebf345beebdb59419ec46d7a12c13d163b935fa16d91199"}