{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C3D5SPI6HB45BA4NIXBUEUZNPL","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":"cc55b7b523446c7dc3a9c598a99cd33fba9ae8127b4ac310008a2ad9ab3e5b1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-11T14:27:13Z","title_canon_sha256":"e4239be3f798c11a09d57077cd5b1c290bb92e84275452ffdc6e710e2810668c"},"schema_version":"1.0","source":{"id":"1301.2506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2506","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2506v1","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2506","created_at":"2026-05-18T03:36:37Z"},{"alias_kind":"pith_short_12","alias_value":"C3D5SPI6HB45","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C3D5SPI6HB45BA4N","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C3D5SPI6","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:2e0915f8fabd70d5a20f5a2e4429d359e51e37c1b25700421bc3f26c9a6c0beb","target":"graph","created_at":"2026-05-18T03:36:37Z","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":"Given a graph $G=(V,E)$ and a set of terminal vertices $T$ we say that a superset $S$ of $T$ is $T$-connecting if $S$ induces a connected graph, and $S$ is minimal if no strict subset of $S$ is $T$-connecting. In this paper we prove that there are at most ${|V \\setminus T| \\choose |T|-2} \\cdot 3^{\\frac{|V \\setminus T|}{3}}$ minimal $T$-connecting sets when $|T| \\leq n/3$ and that these can be enumerated within a polynomial factor of this bound. This generalizes the algorithm for enumerating all induced paths between a pair of vertices, corresponding to the case $|T|=2$. We apply our enumeratio","authors_text":"Jan Arne Telle, Yngve Villanger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-11T14:27:13Z","title":"Connecting Terminals and 2-Disjoint Connected Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2506","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:d198dad4da5bccb1a39d0e3c0f3962106fbeea20eda4ddce7ac1bb9a50dcc926","target":"record","created_at":"2026-05-18T03:36:37Z","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":"cc55b7b523446c7dc3a9c598a99cd33fba9ae8127b4ac310008a2ad9ab3e5b1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-11T14:27:13Z","title_canon_sha256":"e4239be3f798c11a09d57077cd5b1c290bb92e84275452ffdc6e710e2810668c"},"schema_version":"1.0","source":{"id":"1301.2506","kind":"arxiv","version":1}},"canonical_sha256":"16c7d93d1e3879d0838d45c342532d7ac4cd62daee7958e838f161f41e93ba17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16c7d93d1e3879d0838d45c342532d7ac4cd62daee7958e838f161f41e93ba17","first_computed_at":"2026-05-18T03:36:37.714417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:37.714417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zztvVSh0wOVX5LKRX9Gupbr42tDFrz8fPfMBgA+WcWO9vCsuCp98ythgurH7GzR6oPseJWRY4EvDnWKQdLaEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:37.715204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d198dad4da5bccb1a39d0e3c0f3962106fbeea20eda4ddce7ac1bb9a50dcc926","sha256:2e0915f8fabd70d5a20f5a2e4429d359e51e37c1b25700421bc3f26c9a6c0beb"],"state_sha256":"9a40fdcd8d3fa87ff7d46e9d8a73762070799b54b69fa684c45aed93efc0aacc"}