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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-"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0908.1313","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2009-08-10T12:39:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3fbd8a8ffe7976f1fc71d55d439244b1a204866564e308fa4df674c4c88bf4f4","abstract_canon_sha256":"7a4f91dcae14130e7f52e3673972c7603402630903f153471001c0a2dea861f6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:12.039231Z","signature_b64":"/Cl5IvgAo9uhezCSEg30qILwg3as/wUg/0aw50cwruKghLWB87CmUW78SFtEY/UdClp8faE5QxfUEzNeLFG8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0819000683152b19e6a7765d1e0c4bd63b0526332b1ff8bc1b0537e219133130","last_reissued_at":"2026-05-18T04:31:12.038753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:12.038753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Konig-Egervary Square-Stable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Eugen Mandrescu, Vadim E. 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