{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VNHOSXS65JCGTGFY63KCBBQYCT","short_pith_number":"pith:VNHOSXS6","schema_version":"1.0","canonical_sha256":"ab4ee95e5eea446998b8f6d420861814fb00bffb550e7ac252be048d8d456a60","source":{"kind":"arxiv","id":"1806.00386","version":4},"attestation_state":"computed","paper":{"title":"On Efficient Domination for Some Classes of $H$-Free Bipartite 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":"2018-05-30T15:52:09Z","abstract_excerpt":"A vertex set $D$ in a finite undirected graph $G$ is an {\\em efficient dominating set} (\\emph{e.d.s.}\\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \\emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.s.\\ in $G$, is known to be \\NP-complete even for very restricted $H$-free graph classes such as for $2P_3$-free chordal graphs while it is solvable in polynomial time for $P_6$-free graphs. Here we focus on $H$-free bipartite graphs: We show that (weighted) ED can be solved in polynomial time for $H$-free bipartite graphs when"},"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":"1806.00386","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2018-05-30T15:52:09Z","cross_cats_sorted":[],"title_canon_sha256":"e904af43de5bf158852b54b2dabdcfedc3a9f1b5220bc5f5e951abd60ba9103f","abstract_canon_sha256":"449ef209b4de43f49c3f3c95798fa450b32c744b13bc81aacaaf911207a2d9df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:58.561379Z","signature_b64":"CbWwDn/2OD+0XzUCxa0ndAzlaptceHIkV8aiEw0XtTP+63qmZPO0idBCBtjnBmXyYHwRZsBIvOrROG1kCvBkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab4ee95e5eea446998b8f6d420861814fb00bffb550e7ac252be048d8d456a60","last_reissued_at":"2026-05-17T23:39:58.561026Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:58.561026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Efficient Domination for Some Classes of $H$-Free Bipartite 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":"2018-05-30T15:52:09Z","abstract_excerpt":"A vertex set $D$ in a finite undirected graph $G$ is an {\\em efficient dominating set} (\\emph{e.d.s.}\\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \\emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.s.\\ in $G$, is known to be \\NP-complete even for very restricted $H$-free graph classes such as for $2P_3$-free chordal graphs while it is solvable in polynomial time for $P_6$-free graphs. Here we focus on $H$-free bipartite graphs: We show that (weighted) ED can be solved in polynomial time for $H$-free bipartite graphs when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.00386","kind":"arxiv","version":4},"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":"1806.00386","created_at":"2026-05-17T23:39:58.561081+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.00386v4","created_at":"2026-05-17T23:39:58.561081+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.00386","created_at":"2026-05-17T23:39:58.561081+00:00"},{"alias_kind":"pith_short_12","alias_value":"VNHOSXS65JCG","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VNHOSXS65JCGTGFY","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VNHOSXS6","created_at":"2026-05-18T12:32:59.047623+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/VNHOSXS65JCGTGFY63KCBBQYCT","json":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT.json","graph_json":"https://pith.science/api/pith-number/VNHOSXS65JCGTGFY63KCBBQYCT/graph.json","events_json":"https://pith.science/api/pith-number/VNHOSXS65JCGTGFY63KCBBQYCT/events.json","paper":"https://pith.science/paper/VNHOSXS6"},"agent_actions":{"view_html":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT","download_json":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT.json","view_paper":"https://pith.science/paper/VNHOSXS6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.00386&json=true","fetch_graph":"https://pith.science/api/pith-number/VNHOSXS65JCGTGFY63KCBBQYCT/graph.json","fetch_events":"https://pith.science/api/pith-number/VNHOSXS65JCGTGFY63KCBBQYCT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT/action/storage_attestation","attest_author":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT/action/author_attestation","sign_citation":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT/action/citation_signature","submit_replication":"https://pith.science/pith/VNHOSXS65JCGTGFY63KCBBQYCT/action/replication_record"}},"created_at":"2026-05-17T23:39:58.561081+00:00","updated_at":"2026-05-17T23:39:58.561081+00:00"}