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In particular, this means that $M$ is an induced matching, and every edge not in $M$ shares exactly one vertex with an edge in $M$. Clearly, not every graph has a d.i.m.\n  The \\emph{Dominating Induced Matching} (\\emph{DIM}) problem asks for the existence of a d.i.m.\\ in $G$; this problem is also known as the \\emph{Efficient Edge Domination} problem; it is the {\\"},"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":"1706.09301","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-27T15:27:42Z","cross_cats_sorted":[],"title_canon_sha256":"4a899a6039ea5f7e0bb385b323641db5ec1c85a83ea031369c59a7b05b4786ad","abstract_canon_sha256":"3e2f41c3e73de69b7ed584cda116a268dddf3580ae78d640f38e65af211925bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:53.144283Z","signature_b64":"0J10e41M0AvLOJ224cD8N+jC8bD7CcrstmWTx3PYyrbiTg2Fdiysi1do5V7pwpoPvLLWqwJdJTnZrd1zMb5FBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34dcd9550e0b38d70b1421dd3151308e940b01d7f63c862b1522e292297735aa","last_reissued_at":"2026-05-17T23:48:53.143838Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:53.143838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dominating Induced Matchings in $S_{1,2,4}$-Free Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandst\\\"adt, Raffaele Mosca","submitted_at":"2017-06-27T15:27:42Z","abstract_excerpt":"Let $G=(V,E)$ be a finite undirected graph without loops and multiple edges. 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Clearly, not every graph has a d.i.m.\n  The \\emph{Dominating Induced Matching} (\\emph{DIM}) problem asks for the existence of a d.i.m.\\ in $G$; this problem is also known as the \\emph{Efficient Edge Domination} problem; it is the {\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09301","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":"1706.09301","created_at":"2026-05-17T23:48:53.143908+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.09301v3","created_at":"2026-05-17T23:48:53.143908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09301","created_at":"2026-05-17T23:48:53.143908+00:00"},{"alias_kind":"pith_short_12","alias_value":"GTONSVIOBM4N","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"GTONSVIOBM4NOCYU","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"GTONSVIO","created_at":"2026-05-18T12:31:18.294218+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/GTONSVIOBM4NOCYUEHOTCUJQR2","json":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2.json","graph_json":"https://pith.science/api/pith-number/GTONSVIOBM4NOCYUEHOTCUJQR2/graph.json","events_json":"https://pith.science/api/pith-number/GTONSVIOBM4NOCYUEHOTCUJQR2/events.json","paper":"https://pith.science/paper/GTONSVIO"},"agent_actions":{"view_html":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2","download_json":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2.json","view_paper":"https://pith.science/paper/GTONSVIO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.09301&json=true","fetch_graph":"https://pith.science/api/pith-number/GTONSVIOBM4NOCYUEHOTCUJQR2/graph.json","fetch_events":"https://pith.science/api/pith-number/GTONSVIOBM4NOCYUEHOTCUJQR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2/action/storage_attestation","attest_author":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2/action/author_attestation","sign_citation":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2/action/citation_signature","submit_replication":"https://pith.science/pith/GTONSVIOBM4NOCYUEHOTCUJQR2/action/replication_record"}},"created_at":"2026-05-17T23:48:53.143908+00:00","updated_at":"2026-05-17T23:48:53.143908+00:00"}