{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:74ZJR7CNWN66MVSCVZQVQ2FXPN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077"},"schema_version":"1.0","source":{"id":"1407.2053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2053v1","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2053","created_at":"2026-05-18T02:48:08Z"},{"alias_kind":"pith_short_12","alias_value":"74ZJR7CNWN66","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"74ZJR7CNWN66MVSC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"74ZJR7CN","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537","target":"graph","created_at":"2026-05-18T02:48:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A dominating set $D$ in a graph is a subset of its vertex set such that each vertex is either in $D$ or has a neighbour in $D$. In this paper, we are interested in the enumeration of (inclusion-wise) minimal dominating sets in graphs, called the Dom-Enum problem. It is well known that this problem can be polynomially reduced to the Trans-Enum problem in hypergraphs, i.e., the problem of enumerating all minimal transversals in a hypergraph. Firstly we show that the Trans-Enum problem can be polynomially reduced to the Dom-Enum problem. As a consequence there exists an output-polynomial time alg","authors_text":"Arnaud Mary, Lhouari Nourine, Mamadou Moustapha Kant\\'e, Vincent Limouzy","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title":"On the Enumeration of Minimal Dominating Sets and Related Notions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2053","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e","target":"record","created_at":"2026-05-18T02:48:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1f345dfb5c300c9b493dea0677b78a41add88d72ddd75dc725b136ca1a1ffd5b","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-08T12:03:01Z","title_canon_sha256":"e8dc3e5081bf06f422f4d91fe3ebefb6f75261110a01dffaa8d263720476c077"},"schema_version":"1.0","source":{"id":"1407.2053","kind":"arxiv","version":1}},"canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff3298fc4db37de65642ae615868b77b7903e0d0e2de76d1248de834cf0585c1","first_computed_at":"2026-05-18T02:48:08.562850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:08.562850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q5FwM/1eJYLaSvGqaWWs/mKFC1CchCq5n5zD7cxoDbWoqWn3sXyTMoPDfuF6pIbd7XIwWzhUYd6hBn0jgBmNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:08.563377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13238c70bc289922fcc01e372cf3d0710c9b9c41ab1769eb325f7b6650eb274e","sha256:4c11549fe80bbed81f5c0551c0ddd82ba8319f24c1728c316746a9e3f89f9537"],"state_sha256":"c72f47651e3b6792e5fcf2c3ab08747c63570074b203df3ab43c48a89d1ebfd8"}