{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:JXD2BIOR726S6XS3CCDUYTXLQK","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":"cb06ccacd2dabc24c74aa6f6f74625eda6fefeea79ded608d7fc0fd4459f70e3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2008-12-31T17:23:00Z","title_canon_sha256":"e6bc43fb55802ab0b89d331399015346d2c96e132ce778478cc91227d1de80dc"},"schema_version":"1.0","source":{"id":"0901.0121","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0121","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0121v3","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0121","created_at":"2026-05-18T04:08:13Z"},{"alias_kind":"pith_short_12","alias_value":"JXD2BIOR726S","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"JXD2BIOR726S6XS3","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"JXD2BIOR","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:406121938e51af50393045e212e8df19675612a2e1013309254576dfd4e4349d","target":"graph","created_at":"2026-05-18T04:08:13Z","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":"For a graph $G$ let $L(G)$ and $l(G)$ denote the size of the largest and smallest maximum matching of a graph obtained from $G$ by removing a maximum matching of $G$. We show that $L(G)\\leq 2l(G),$ and $L(G)\\leq (3/2)l(G)$ provided that $G$ contains a perfect matching. We also characterize the class of graphs for which $L(G)=2l(G)$. Our characterization implies the existence of a polynomial algorithm for testing the property $L(G)=2l(G)$. Finally we show that it is $NP$-complete to test whether a graph $G$ containing a perfect matching satisfies $L(G)=(3/2)l(G)$.","authors_text":"Artur Khojabaghyan, Vahan V. Mkrtchyan","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2008-12-31T17:23:00Z","title":"On upper bounds for parameters related to construction of special maximum matchings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0121","kind":"arxiv","version":3},"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:f85e760faf612d8fdd0698a6c076db33f88122024cca8c746a91a88bc927e788","target":"record","created_at":"2026-05-18T04:08:13Z","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":"cb06ccacd2dabc24c74aa6f6f74625eda6fefeea79ded608d7fc0fd4459f70e3","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2008-12-31T17:23:00Z","title_canon_sha256":"e6bc43fb55802ab0b89d331399015346d2c96e132ce778478cc91227d1de80dc"},"schema_version":"1.0","source":{"id":"0901.0121","kind":"arxiv","version":3}},"canonical_sha256":"4dc7a0a1d1febd2f5e5b10874c4eeb82b782eec5af28e0ae2e96db35d9dd2a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4dc7a0a1d1febd2f5e5b10874c4eeb82b782eec5af28e0ae2e96db35d9dd2a7b","first_computed_at":"2026-05-18T04:08:13.677828Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:13.677828Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"br2doByq3QNW/lxS8ZNr3AIwc5XAG0W2555W6JO3OeQYO1gUm5rDNorqMzP4B2FIHkzsnR2YEaGab7aA3ChkDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:13.678252Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0121","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f85e760faf612d8fdd0698a6c076db33f88122024cca8c746a91a88bc927e788","sha256:406121938e51af50393045e212e8df19675612a2e1013309254576dfd4e4349d"],"state_sha256":"775de0cbdcdd1a2d8bc70edfa38599887d04af64c66d18d9662ab575f729ead6"}