{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MUJM6OKFNCCYSVEW2WBN6QKZRS","short_pith_number":"pith:MUJM6OKF","schema_version":"1.0","canonical_sha256":"6512cf39456885895496d582df41598cb5b9e732f82bf8617d0cd2219a1ac607","source":{"kind":"arxiv","id":"1304.6153","version":1},"attestation_state":"computed","paper":{"title":"Further hardness results on the generalized connectivity of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lily Chen, Mengmeng Liu, Xueliang Li, Yaping Mao","submitted_at":"2013-04-23T02:50:34Z","abstract_excerpt":"The generalized $k$-connectivity $\\kappa_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984, which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we determine the computational complexity of the generalized connectivity and generalized edge-connectivity of a graph. Two conjectures are also proved to be true."},"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":"1304.6153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-23T02:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"f56d3faa326de1eab0296151f643d45c782c87172d02d8be85bde1011525cc0f","abstract_canon_sha256":"ede974e4a6ad45b4d79ab04ff2db526f67c10e3d3b73250284b7bd8a5363e229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:22.271284Z","signature_b64":"L8BX6DLhK8UzvY/hhv3urLLtjRGgRdKK/oP67PD0KrEarfOa5YX6Qa84VlBZSKaxFgkdVWGxa42TAPXcpA9iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6512cf39456885895496d582df41598cb5b9e732f82bf8617d0cd2219a1ac607","last_reissued_at":"2026-05-18T03:27:22.270588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:22.270588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Further hardness results on the generalized connectivity of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lily Chen, Mengmeng Liu, Xueliang Li, Yaping Mao","submitted_at":"2013-04-23T02:50:34Z","abstract_excerpt":"The generalized $k$-connectivity $\\kappa_k(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984, which is a nice generalization of the classical connectivity. Recently, as a natural counterpart, Li et al. proposed the concept of generalized edge-connectivity for a graph. In this paper, we determine the computational complexity of the generalized connectivity and generalized edge-connectivity of a graph. Two conjectures are also proved to be true."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6153","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":"1304.6153","created_at":"2026-05-18T03:27:22.270717+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.6153v1","created_at":"2026-05-18T03:27:22.270717+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6153","created_at":"2026-05-18T03:27:22.270717+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUJM6OKFNCCY","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUJM6OKFNCCYSVEW","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUJM6OKF","created_at":"2026-05-18T12:27:52.871228+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/MUJM6OKFNCCYSVEW2WBN6QKZRS","json":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS.json","graph_json":"https://pith.science/api/pith-number/MUJM6OKFNCCYSVEW2WBN6QKZRS/graph.json","events_json":"https://pith.science/api/pith-number/MUJM6OKFNCCYSVEW2WBN6QKZRS/events.json","paper":"https://pith.science/paper/MUJM6OKF"},"agent_actions":{"view_html":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS","download_json":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS.json","view_paper":"https://pith.science/paper/MUJM6OKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.6153&json=true","fetch_graph":"https://pith.science/api/pith-number/MUJM6OKFNCCYSVEW2WBN6QKZRS/graph.json","fetch_events":"https://pith.science/api/pith-number/MUJM6OKFNCCYSVEW2WBN6QKZRS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS/action/storage_attestation","attest_author":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS/action/author_attestation","sign_citation":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS/action/citation_signature","submit_replication":"https://pith.science/pith/MUJM6OKFNCCYSVEW2WBN6QKZRS/action/replication_record"}},"created_at":"2026-05-18T03:27:22.270717+00:00","updated_at":"2026-05-18T03:27:22.270717+00:00"}