{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:D62CVX3TJEMUZQZLGFWGFRAVXC","short_pith_number":"pith:D62CVX3T","schema_version":"1.0","canonical_sha256":"1fb42adf7349194cc32b316c62c415b8aa836e00a1f6fed16ad7129319237080","source":{"kind":"arxiv","id":"1602.09127","version":3},"attestation_state":"computed","paper":{"title":"Edge-Stable Equimatchable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"T{\\i}naz Ekim, Zakir Deniz","submitted_at":"2016-02-29T20:28:24Z","abstract_excerpt":"A graph $G$ is \\emph{equimatchable} if every maximal matching of $G$ has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph $G$ \\emph{edge-stable} if $G\\setminus {e}$, that is the graph obtained by the removal of edge $e$ from $G$, is also equimatchable for any $e \\in E(G)$. After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartite, we characterize edge-stable equimatchable graphs. This characterization yields an $O(\\min(n^{"},"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":"1602.09127","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-02-29T20:28:24Z","cross_cats_sorted":[],"title_canon_sha256":"04652430e69d639afb806ae2113f7014e2a79db49d4bfcb2947f7c6bb33eea8d","abstract_canon_sha256":"24a27fefda66ea9344e719c0b25d5dcce7d41f51ead63ac0c3f7ad8ea4b0e4d3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:19.795592Z","signature_b64":"Zqt18MpbqOwBdTal1Rt7uNwpgtHLS1kNSjVyQQ6gvV+b4S6md3Ep4mFX0vgO4Mnuz6R8lsJ0mXFwr3hcFc4WBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb42adf7349194cc32b316c62c415b8aa836e00a1f6fed16ad7129319237080","last_reissued_at":"2026-05-18T00:13:19.794921Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:19.794921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Edge-Stable Equimatchable Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"T{\\i}naz Ekim, Zakir Deniz","submitted_at":"2016-02-29T20:28:24Z","abstract_excerpt":"A graph $G$ is \\emph{equimatchable} if every maximal matching of $G$ has the same cardinality. We are interested in equimatchable graphs such that the removal of any edge from the graph preserves the equimatchability. We call an equimatchable graph $G$ \\emph{edge-stable} if $G\\setminus {e}$, that is the graph obtained by the removal of edge $e$ from $G$, is also equimatchable for any $e \\in E(G)$. After noticing that edge-stable equimatchable graphs are either 2-connected factor-critical or bipartite, we characterize edge-stable equimatchable graphs. This characterization yields an $O(\\min(n^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09127","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.09127","created_at":"2026-05-18T00:13:19.795035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.09127v3","created_at":"2026-05-18T00:13:19.795035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.09127","created_at":"2026-05-18T00:13:19.795035+00:00"},{"alias_kind":"pith_short_12","alias_value":"D62CVX3TJEMU","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"D62CVX3TJEMUZQZL","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"D62CVX3T","created_at":"2026-05-18T12:30:09.641336+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC","json":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC.json","graph_json":"https://pith.science/api/pith-number/D62CVX3TJEMUZQZLGFWGFRAVXC/graph.json","events_json":"https://pith.science/api/pith-number/D62CVX3TJEMUZQZLGFWGFRAVXC/events.json","paper":"https://pith.science/paper/D62CVX3T"},"agent_actions":{"view_html":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC","download_json":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC.json","view_paper":"https://pith.science/paper/D62CVX3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.09127&json=true","fetch_graph":"https://pith.science/api/pith-number/D62CVX3TJEMUZQZLGFWGFRAVXC/graph.json","fetch_events":"https://pith.science/api/pith-number/D62CVX3TJEMUZQZLGFWGFRAVXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC/action/storage_attestation","attest_author":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC/action/author_attestation","sign_citation":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC/action/citation_signature","submit_replication":"https://pith.science/pith/D62CVX3TJEMUZQZLGFWGFRAVXC/action/replication_record"}},"created_at":"2026-05-18T00:13:19.795035+00:00","updated_at":"2026-05-18T00:13:19.795035+00:00"}