{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BAMQABUDCUVRTZVHOZOR4DCL2Y","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":"7a4f91dcae14130e7f52e3673972c7603402630903f153471001c0a2dea861f6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-10T12:39:31Z","title_canon_sha256":"3fbd8a8ffe7976f1fc71d55d439244b1a204866564e308fa4df674c4c88bf4f4"},"schema_version":"1.0","source":{"id":"0908.1313","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.1313","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"0908.1313v3","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.1313","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"BAMQABUDCUVR","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BAMQABUDCUVRTZVH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BAMQABUD","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:40cb638c481f29906355198c6e8250e95e4b62f1a93dc33837d148b5b875873d","target":"graph","created_at":"2026-05-18T04:31:12Z","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":"The stability number of a graph G, denoted by alpha(G), is the cardinality of a maximum stable set, and mu(G) is the cardinality of a maximum matching in G. If alpha(G)+mu(G) equals its order, then G is a Konig-Egervary graph.\n  In this paper we deal with square-stable graphs, i.e., the graphs G enjoying the equality alpha(G)=alpha(G^{2}), where G^{2} denotes the second power of G. In particular, we show that a Konig-Egervary graph is square-stable if and only if it has a perfect matching consisting of pendant edges, and in consequence, we deduce that well-covered trees are exactly the square-","authors_text":"Eugen Mandrescu, Vadim E. Levit","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-10T12:39:31Z","title":"On Konig-Egervary Square-Stable Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.1313","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":"sha256:04970ec563dc40e354daa44071d41daa0c0af4b7f9d176aa55358ae65d3d0778","target":"record","created_at":"2026-05-18T04:31:12Z","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":"7a4f91dcae14130e7f52e3673972c7603402630903f153471001c0a2dea861f6","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-10T12:39:31Z","title_canon_sha256":"3fbd8a8ffe7976f1fc71d55d439244b1a204866564e308fa4df674c4c88bf4f4"},"schema_version":"1.0","source":{"id":"0908.1313","kind":"arxiv","version":3}},"canonical_sha256":"0819000683152b19e6a7765d1e0c4bd63b0526332b1ff8bc1b0537e219133130","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0819000683152b19e6a7765d1e0c4bd63b0526332b1ff8bc1b0537e219133130","first_computed_at":"2026-05-18T04:31:12.038753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:12.038753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Cl5IvgAo9uhezCSEg30qILwg3as/wUg/0aw50cwruKghLWB87CmUW78SFtEY/UdClp8faE5QxfUEzNeLFG8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:12.039231Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.1313","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:04970ec563dc40e354daa44071d41daa0c0af4b7f9d176aa55358ae65d3d0778","sha256:40cb638c481f29906355198c6e8250e95e4b62f1a93dc33837d148b5b875873d"],"state_sha256":"30413f5a81b1809abc1231a0b95382acc8fa6cadfb4eee08cefe52c3e0225751"}