{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6N3MXUXSEOM4R6MKCTOLWWZYND","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":"410dc20e081a28ebd6df9b2873aa3d3d8e86c051f87b17497544958dcdcaaead","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2012-02-03T12:39:14Z","title_canon_sha256":"a5e59190325caa132d4aa2e2c11bbca5a1a52665e0b1ec96bb47fdcfec834fd6"},"schema_version":"1.0","source":{"id":"1202.0681","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.0681","created_at":"2026-05-18T03:49:00Z"},{"alias_kind":"arxiv_version","alias_value":"1202.0681v2","created_at":"2026-05-18T03:49:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.0681","created_at":"2026-05-18T03:49:00Z"},{"alias_kind":"pith_short_12","alias_value":"6N3MXUXSEOM4","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6N3MXUXSEOM4R6MK","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6N3MXUXS","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:4114e62cd195ae1097b2d8b7017f5a6c671f7a18b1d900e9d8aa01c43cb31917","target":"graph","created_at":"2026-05-18T03:49:00Z","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 2010, Mkrtchyan, Petrosyan and Vardanyan proved that every graph $G$ with $2\\leq \\delta(G)\\leq \\Delta(G)\\leq 3$ contains a maximum matching whose unsaturated vertices do not have a common neighbor, where $\\Delta(G)$ and $\\delta(G)$ denote the maximum and minimum degrees of vertices in $G$, respectively. In the same paper they suggested the following conjecture: every graph $G$ with $\\Delta(G)-\\delta(G)\\leq 1$ contains a maximum matching whose unsaturated vertices do not have a common neighbor. Recently, Picouleau disproved this conjecture by constructing a bipartite counterexample $G$ with ","authors_text":"Petros A. Petrosyan","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2012-02-03T12:39:14Z","title":"On maximum matchings in almost regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.0681","kind":"arxiv","version":2},"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":"sha256:3b2cbaba175f37bc87c87592bea83d9fa013c0cadfee7cb15e05c30b16892ec2","target":"record","created_at":"2026-05-18T03:49:00Z","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":"410dc20e081a28ebd6df9b2873aa3d3d8e86c051f87b17497544958dcdcaaead","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2012-02-03T12:39:14Z","title_canon_sha256":"a5e59190325caa132d4aa2e2c11bbca5a1a52665e0b1ec96bb47fdcfec834fd6"},"schema_version":"1.0","source":{"id":"1202.0681","kind":"arxiv","version":2}},"canonical_sha256":"f376cbd2f22399c8f98a14dcbb5b3868cbc6cbb6ca54a0676679a311208f5b9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f376cbd2f22399c8f98a14dcbb5b3868cbc6cbb6ca54a0676679a311208f5b9b","first_computed_at":"2026-05-18T03:49:00.962117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:00.962117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSqYSwl6W5KFb6hRbH+n2qi81XHtMxbpc6xiiiQJpkfxIlwgR9iKuQg2O4Scp0lrcZ/+IacntglS0fsoFTNmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:00.962760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.0681","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b2cbaba175f37bc87c87592bea83d9fa013c0cadfee7cb15e05c30b16892ec2","sha256:4114e62cd195ae1097b2d8b7017f5a6c671f7a18b1d900e9d8aa01c43cb31917"],"state_sha256":"ba6853217b33b4f62b9db7d3325283a1dd1ffaddefa53d4448b35e5436298dcd"}