{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:CKUBQ7WJUHJPDFPIDKFDC55H7N","short_pith_number":"pith:CKUBQ7WJ","schema_version":"1.0","canonical_sha256":"12a8187ec9a1d2f195e81a8a3177a7fb5277b6ae447e9572aceda9a74880ad3d","source":{"kind":"arxiv","id":"1303.5171","version":1},"attestation_state":"computed","paper":{"title":"The generalized 3-connectivity of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li, Yongtang Shi","submitted_at":"2013-03-21T05:40:07Z","abstract_excerpt":"The generalized connectivity of a graph $G$ was introduced by Chartrand et al. Let $S$ be a nonempty set of vertices of $G$, and $\\kappa(S)$ be defined as the largest number of internally disjoint trees $T_1, T_2, \\cdots, T_k$ connecting $S$ in $G$. Then for an integer $r$ with $2 \\leq r \\leq n$, the {\\it generalized $r$-connectivity} $\\kappa_r(G)$ of $G$ is the minimum $\\kappa(S)$ where $S$ runs over all the $r$-subsets of the vertex set of $G$. Obviously, $\\kappa_2(G)=\\kappa(G)$, is the vertex connectivity of $G$, and hence the generalized connectivity is a natural generalization of the vert"},"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":"1303.5171","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-21T05:40:07Z","cross_cats_sorted":[],"title_canon_sha256":"35fd3a0cd18822bb2c448678882ac2b035834cf6a4ad66936ab42c5005f41125","abstract_canon_sha256":"b5042bebaf5f66b25109897948585f658dab3ed6c76c9590a0790eea6eef25df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:14.293118Z","signature_b64":"3GjtyCaGp+KskAjtxLg2eQ/KxvKR3eTY6/sHGSR6QudgpKduPn3M5rKhfu9MLCSKaUGmODEYP8D9XE8laZzfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12a8187ec9a1d2f195e81a8a3177a7fb5277b6ae447e9572aceda9a74880ad3d","last_reissued_at":"2026-05-18T03:30:14.292303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:14.292303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The generalized 3-connectivity of random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ran Gu, Xueliang Li, Yongtang Shi","submitted_at":"2013-03-21T05:40:07Z","abstract_excerpt":"The generalized connectivity of a graph $G$ was introduced by Chartrand et al. Let $S$ be a nonempty set of vertices of $G$, and $\\kappa(S)$ be defined as the largest number of internally disjoint trees $T_1, T_2, \\cdots, T_k$ connecting $S$ in $G$. Then for an integer $r$ with $2 \\leq r \\leq n$, the {\\it generalized $r$-connectivity} $\\kappa_r(G)$ of $G$ is the minimum $\\kappa(S)$ where $S$ runs over all the $r$-subsets of the vertex set of $G$. Obviously, $\\kappa_2(G)=\\kappa(G)$, is the vertex connectivity of $G$, and hence the generalized connectivity is a natural generalization of the vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5171","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":"1303.5171","created_at":"2026-05-18T03:30:14.292442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.5171v1","created_at":"2026-05-18T03:30:14.292442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.5171","created_at":"2026-05-18T03:30:14.292442+00:00"},{"alias_kind":"pith_short_12","alias_value":"CKUBQ7WJUHJP","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"CKUBQ7WJUHJPDFPI","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"CKUBQ7WJ","created_at":"2026-05-18T12:27:40.988391+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/CKUBQ7WJUHJPDFPIDKFDC55H7N","json":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N.json","graph_json":"https://pith.science/api/pith-number/CKUBQ7WJUHJPDFPIDKFDC55H7N/graph.json","events_json":"https://pith.science/api/pith-number/CKUBQ7WJUHJPDFPIDKFDC55H7N/events.json","paper":"https://pith.science/paper/CKUBQ7WJ"},"agent_actions":{"view_html":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N","download_json":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N.json","view_paper":"https://pith.science/paper/CKUBQ7WJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.5171&json=true","fetch_graph":"https://pith.science/api/pith-number/CKUBQ7WJUHJPDFPIDKFDC55H7N/graph.json","fetch_events":"https://pith.science/api/pith-number/CKUBQ7WJUHJPDFPIDKFDC55H7N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N/action/storage_attestation","attest_author":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N/action/author_attestation","sign_citation":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N/action/citation_signature","submit_replication":"https://pith.science/pith/CKUBQ7WJUHJPDFPIDKFDC55H7N/action/replication_record"}},"created_at":"2026-05-18T03:30:14.292442+00:00","updated_at":"2026-05-18T03:30:14.292442+00:00"}