{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:NU2MGUPT7HZXDHBKXUAFB2U2B5","short_pith_number":"pith:NU2MGUPT","schema_version":"1.0","canonical_sha256":"6d34c351f3f9f3719c2abd0050ea9a0f4016cb496f47446c6393fb410b643811","source":{"kind":"arxiv","id":"1705.08379","version":1},"attestation_state":"computed","paper":{"title":"Perfect Edge Domination: Hard and Solvable Cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jayme L. Szwarcfiter, Min Chih Lin, Vadim Lozin, Veronica A. Moyano","submitted_at":"2017-05-23T15:53:04Z","abstract_excerpt":"Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is a perfect edge dominating set of $G$, if every edge not in $E'$ is dominated by exactly one edge of $E'$. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of $G$. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, "},"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":"1705.08379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-23T15:53:04Z","cross_cats_sorted":[],"title_canon_sha256":"1de6da0fcf8d81421ceb7bdb14d2bf9f3965f50b2c40829dbc13871598a336a9","abstract_canon_sha256":"14927fa9579b3193f37ad0c6bd32705d2eda6f45a513fe455d1514b9b2dfce11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:48.429964Z","signature_b64":"dk6g2oOrBqZG8JMsdVR6xjbPbfSnsFPJ0Mm5e85ruc1Ljsm2wPnQjHFfWyKDLVX+FkfGCQZpEm8aOvAVkDL3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d34c351f3f9f3719c2abd0050ea9a0f4016cb496f47446c6393fb410b643811","last_reissued_at":"2026-05-18T00:43:48.429507Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:48.429507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perfect Edge Domination: Hard and Solvable Cases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Jayme L. Szwarcfiter, Min Chih Lin, Vadim Lozin, Veronica A. Moyano","submitted_at":"2017-05-23T15:53:04Z","abstract_excerpt":"Let $G$ be an undirected graph. An edge of $G$ dominates itself and all edges adjacent to it. A subset $E'$ of edges of $G$ is an edge dominating set of $G$, if every edge of the graph is dominated by some edge of $E'$. We say that $E'$ is a perfect edge dominating set of $G$, if every edge not in $E'$ is dominated by exactly one edge of $E'$. The perfect edge dominating problem is to determine a least cardinality perfect edge dominating set of $G$. For this problem, we describe two NP-completeness proofs, for the classes of claw-free graphs of degree at most 3, and for bounded degree graphs, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08379","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":"1705.08379","created_at":"2026-05-18T00:43:48.429580+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08379v1","created_at":"2026-05-18T00:43:48.429580+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08379","created_at":"2026-05-18T00:43:48.429580+00:00"},{"alias_kind":"pith_short_12","alias_value":"NU2MGUPT7HZX","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"NU2MGUPT7HZXDHBK","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"NU2MGUPT","created_at":"2026-05-18T12:31:34.259226+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/NU2MGUPT7HZXDHBKXUAFB2U2B5","json":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5.json","graph_json":"https://pith.science/api/pith-number/NU2MGUPT7HZXDHBKXUAFB2U2B5/graph.json","events_json":"https://pith.science/api/pith-number/NU2MGUPT7HZXDHBKXUAFB2U2B5/events.json","paper":"https://pith.science/paper/NU2MGUPT"},"agent_actions":{"view_html":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5","download_json":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5.json","view_paper":"https://pith.science/paper/NU2MGUPT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08379&json=true","fetch_graph":"https://pith.science/api/pith-number/NU2MGUPT7HZXDHBKXUAFB2U2B5/graph.json","fetch_events":"https://pith.science/api/pith-number/NU2MGUPT7HZXDHBKXUAFB2U2B5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5/action/storage_attestation","attest_author":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5/action/author_attestation","sign_citation":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5/action/citation_signature","submit_replication":"https://pith.science/pith/NU2MGUPT7HZXDHBKXUAFB2U2B5/action/replication_record"}},"created_at":"2026-05-18T00:43:48.429580+00:00","updated_at":"2026-05-18T00:43:48.429580+00:00"}