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The matching $M$ is induced, if $G(M)$ is $1$-regular, and $M$ is uniquely restricted, if $M$ is the unique perfect matching of $G(M)$. The induced matching number $\\nu_s(G)$ of $G$ is the largest size of an induced matching in $G$, and the uniquely restricted matching number $\\nu_{ur}(G)$ of $G$ is the largest size of a uniquely restricted matching in $G$.\n  Golumbic, Hirst, and Lewenstein (Uniquely restricted matchings, Algorithmica 31 (2001) 139-154) pos"},"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":"1807.08981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-24T09:17:05Z","cross_cats_sorted":[],"title_canon_sha256":"e9f44f8e5f2334cc9fb64d929f9f21e3b523f192f9cea97b8692840ba0e204c7","abstract_canon_sha256":"cb6e4c1893f47562dd1510e52e4584494db7eb405093f75ed190811be0a2d002"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:57.168258Z","signature_b64":"LeUbHI/Pym8lcLOdng2NAAFuSNl43NCLywltbJCJWptcb0lQuqF8aAtVm43lZKNSR9hzl9YTDqAD1pfbM6KmDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"991ed8816f4f62e94d03490e3a57583e7753e7c396d123552ad75277e4a04932","last_reissued_at":"2026-05-18T00:09:57.167641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:57.167641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the equality of the induced matching number and the uniquely restricted matching number for subcubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"D. 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The induced matching number $\\nu_s(G)$ of $G$ is the largest size of an induced matching in $G$, and the uniquely restricted matching number $\\nu_{ur}(G)$ of $G$ is the largest size of a uniquely restricted matching in $G$.\n  Golumbic, Hirst, and Lewenstein (Uniquely restricted matchings, Algorithmica 31 (2001) 139-154) pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08981","kind":"arxiv","version":1},"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":"1807.08981","created_at":"2026-05-18T00:09:57.167724+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.08981v1","created_at":"2026-05-18T00:09:57.167724+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08981","created_at":"2026-05-18T00:09:57.167724+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEPNRALPJ5RO","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEPNRALPJ5ROSTID","created_at":"2026-05-18T12:32:53.628368+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEPNRALP","created_at":"2026-05-18T12:32:53.628368+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/TEPNRALPJ5ROSTIDJEHDUV2YHZ","json":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ.json","graph_json":"https://pith.science/api/pith-number/TEPNRALPJ5ROSTIDJEHDUV2YHZ/graph.json","events_json":"https://pith.science/api/pith-number/TEPNRALPJ5ROSTIDJEHDUV2YHZ/events.json","paper":"https://pith.science/paper/TEPNRALP"},"agent_actions":{"view_html":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ","download_json":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ.json","view_paper":"https://pith.science/paper/TEPNRALP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.08981&json=true","fetch_graph":"https://pith.science/api/pith-number/TEPNRALPJ5ROSTIDJEHDUV2YHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/TEPNRALPJ5ROSTIDJEHDUV2YHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ/action/storage_attestation","attest_author":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ/action/author_attestation","sign_citation":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ/action/citation_signature","submit_replication":"https://pith.science/pith/TEPNRALPJ5ROSTIDJEHDUV2YHZ/action/replication_record"}},"created_at":"2026-05-18T00:09:57.167724+00:00","updated_at":"2026-05-18T00:09:57.167724+00:00"}