{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I3JYWIWSGC5DRTDZOKN2C2MHIJ","short_pith_number":"pith:I3JYWIWS","schema_version":"1.0","canonical_sha256":"46d38b22d230ba38cc79729ba16987427df8d46b9779da65689b8f228f357634","source":{"kind":"arxiv","id":"1606.01693","version":2},"attestation_state":"computed","paper":{"title":"Polyhedra with few 3-cuts are hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carol T. Zamfirescu, Gunnar Brinkmann","submitted_at":"2016-06-06T11:30:45Z","abstract_excerpt":"In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four 3-cuts have a hamiltonian path. It is well known that for each $k \\ge 6$ non-hamiltonian polyhedra with $k$ 3-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five"},"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":"1606.01693","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-06T11:30:45Z","cross_cats_sorted":[],"title_canon_sha256":"2193d83a9eafa6ea88a5fe092df5e30efbf64ea6f5265b69716ffbd4eca139fc","abstract_canon_sha256":"8a65e90fd0139b86051d693fc5868409556a45b0ecb2825857496b8d3dd00d7d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:23.084569Z","signature_b64":"NU6JN4VG/SYTknVq3ZUhaTdR8kznDcZXcMqQWj4TXC5LSaUFDfp/sqm1wsmMxpjJawKjWWYqRrpNXC/JBZjkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46d38b22d230ba38cc79729ba16987427df8d46b9779da65689b8f228f357634","last_reissued_at":"2026-05-18T00:14:23.083754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:23.083754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polyhedra with few 3-cuts are hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carol T. Zamfirescu, Gunnar Brinkmann","submitted_at":"2016-06-06T11:30:45Z","abstract_excerpt":"In 1956, Tutte showed that every planar 4-connected graph is hamiltonian. In this article, we will generalize this result and prove that polyhedra with at most three 3-cuts are hamiltonian. In 2002 Jackson and Yu have shown this result for the subclass of triangulations. We also prove that polyhedra with at most four 3-cuts have a hamiltonian path. It is well known that for each $k \\ge 6$ non-hamiltonian polyhedra with $k$ 3-cuts exist. We give computational results on lower bounds on the order of a possible non-hamiltonian polyhedron for the remaining open cases of polyhedra with four or five"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01693","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":"1606.01693","created_at":"2026-05-18T00:14:23.083864+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.01693v2","created_at":"2026-05-18T00:14:23.083864+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01693","created_at":"2026-05-18T00:14:23.083864+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3JYWIWSGC5D","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3JYWIWSGC5DRTDZ","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3JYWIWS","created_at":"2026-05-18T12:30:22.444734+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/I3JYWIWSGC5DRTDZOKN2C2MHIJ","json":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ.json","graph_json":"https://pith.science/api/pith-number/I3JYWIWSGC5DRTDZOKN2C2MHIJ/graph.json","events_json":"https://pith.science/api/pith-number/I3JYWIWSGC5DRTDZOKN2C2MHIJ/events.json","paper":"https://pith.science/paper/I3JYWIWS"},"agent_actions":{"view_html":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ","download_json":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ.json","view_paper":"https://pith.science/paper/I3JYWIWS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.01693&json=true","fetch_graph":"https://pith.science/api/pith-number/I3JYWIWSGC5DRTDZOKN2C2MHIJ/graph.json","fetch_events":"https://pith.science/api/pith-number/I3JYWIWSGC5DRTDZOKN2C2MHIJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ/action/storage_attestation","attest_author":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ/action/author_attestation","sign_citation":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ/action/citation_signature","submit_replication":"https://pith.science/pith/I3JYWIWSGC5DRTDZOKN2C2MHIJ/action/replication_record"}},"created_at":"2026-05-18T00:14:23.083864+00:00","updated_at":"2026-05-18T00:14:23.083864+00:00"}