{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:U3GKIQ3FSLL6JN3VLDNLCJTCVC","short_pith_number":"pith:U3GKIQ3F","schema_version":"1.0","canonical_sha256":"a6cca4436592d7e4b77558dab12662a89dee9b0acad7289b1b9ccf7a44179234","source":{"kind":"arxiv","id":"1805.08461","version":2},"attestation_state":"computed","paper":{"title":"The restricted $h$-connectivity of balanced hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huazhong L\\\"u, Tingzeng Wu","submitted_at":"2018-05-22T09:02:56Z","abstract_excerpt":"The restricted $h$-connectivity of a graph $G$, denoted by $\\kappa^h(G)$, is defined as the minimum cardinality of a set of vertices $F$ in $G$, if exists, whose removal disconnects $G$ and the minimum degree of each component of $G-F$ is at least $h$. In this paper, we study the restricted $h$-connectivity of the balanced hypercube $BH_n$ and determine that $\\kappa^1(BH_n)=\\kappa^2(BH_n)=4n-4$ for $n\\geq2$. We also obtain a sharp upper bound of $\\kappa^3(BH_n)$ and $\\kappa^4(BH_n)$ of $n$-dimension balanced hypercube for $n\\geq3$ ($n\\neq4$). In particular, we show that $\\kappa^3(BH_3)=\\kappa^"},"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":"1805.08461","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-05-22T09:02:56Z","cross_cats_sorted":[],"title_canon_sha256":"bc51e06d7cc665522b02bf9d26e72cfa22287bb2878c32d290be236a5f7438f1","abstract_canon_sha256":"3d8e8c86293d2ff91f31926737c548a63fac10fb36cb4f8af410004ea301a9ea"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:33.687987Z","signature_b64":"zg66m8JfJYfsBUfFU5ESkG+Gr+r2kJKoHy3b0Ytx9hcRXDSa34fX2UvjqOmNiGHatg2Z/HD/zMIl49qySQifAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6cca4436592d7e4b77558dab12662a89dee9b0acad7289b1b9ccf7a44179234","last_reissued_at":"2026-05-18T00:14:33.687331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:33.687331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The restricted $h$-connectivity of balanced hypercubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huazhong L\\\"u, Tingzeng Wu","submitted_at":"2018-05-22T09:02:56Z","abstract_excerpt":"The restricted $h$-connectivity of a graph $G$, denoted by $\\kappa^h(G)$, is defined as the minimum cardinality of a set of vertices $F$ in $G$, if exists, whose removal disconnects $G$ and the minimum degree of each component of $G-F$ is at least $h$. In this paper, we study the restricted $h$-connectivity of the balanced hypercube $BH_n$ and determine that $\\kappa^1(BH_n)=\\kappa^2(BH_n)=4n-4$ for $n\\geq2$. We also obtain a sharp upper bound of $\\kappa^3(BH_n)$ and $\\kappa^4(BH_n)$ of $n$-dimension balanced hypercube for $n\\geq3$ ($n\\neq4$). In particular, we show that $\\kappa^3(BH_3)=\\kappa^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08461","kind":"arxiv","version":2},"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":"1805.08461","created_at":"2026-05-18T00:14:33.687453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.08461v2","created_at":"2026-05-18T00:14:33.687453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08461","created_at":"2026-05-18T00:14:33.687453+00:00"},{"alias_kind":"pith_short_12","alias_value":"U3GKIQ3FSLL6","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"U3GKIQ3FSLL6JN3V","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"U3GKIQ3F","created_at":"2026-05-18T12:32:56.356000+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/U3GKIQ3FSLL6JN3VLDNLCJTCVC","json":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC.json","graph_json":"https://pith.science/api/pith-number/U3GKIQ3FSLL6JN3VLDNLCJTCVC/graph.json","events_json":"https://pith.science/api/pith-number/U3GKIQ3FSLL6JN3VLDNLCJTCVC/events.json","paper":"https://pith.science/paper/U3GKIQ3F"},"agent_actions":{"view_html":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC","download_json":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC.json","view_paper":"https://pith.science/paper/U3GKIQ3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.08461&json=true","fetch_graph":"https://pith.science/api/pith-number/U3GKIQ3FSLL6JN3VLDNLCJTCVC/graph.json","fetch_events":"https://pith.science/api/pith-number/U3GKIQ3FSLL6JN3VLDNLCJTCVC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC/action/storage_attestation","attest_author":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC/action/author_attestation","sign_citation":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC/action/citation_signature","submit_replication":"https://pith.science/pith/U3GKIQ3FSLL6JN3VLDNLCJTCVC/action/replication_record"}},"created_at":"2026-05-18T00:14:33.687453+00:00","updated_at":"2026-05-18T00:14:33.687453+00:00"}