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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 Efficient Domination problem for line graphs.\n  The DIM problem is \\NP-complete even for very restricted graph classes such as planar bipartite graphs with maximum degree 3 but is solvable in linear time for $P_"},"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":"1905.05582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-05-14T13:17:00Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"abc9e9b4acf723bebe3b16c75a918213633f97afc98c0e8145aa8f39effe6d36","abstract_canon_sha256":"3841a8896c92795dbdf1104376f837eeaaf0aba113f0e94be1741e16694eaa93"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:07.577546Z","signature_b64":"OQNyQrnqXRNtpczE/Rm7vKnuNA6DZFaHuD5/YL14p8PpqHP1N2+YtSI07y6Jd6b7euBgnGHX2+atPYxR38Y+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2f3782fa1bb8e10ed249a4776ee7eea21181181fe8b129a7440a3bad61b91e8","last_reissued_at":"2026-07-05T00:49:07.577147Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:07.577147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finding Dominating Induced Matchings in $S_{1,1,5}$-Free Graphs in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Andreas Brandst\\\"adt, Raffaele Mosca","submitted_at":"2019-05-14T13:17:00Z","abstract_excerpt":"Let $G=(V,E)$ be a finite undirected graph. 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