{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DHWLP4F46LRPAO755EHRCKEU6C","short_pith_number":"pith:DHWLP4F4","schema_version":"1.0","canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","source":{"kind":"arxiv","id":"1901.10683","version":2},"attestation_state":"computed","paper":{"title":"Highly-connected planar cubic graphs with few or many Hamilton cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gordon Royle, Irene Pivotto","submitted_at":"2019-01-30T06:13:41Z","abstract_excerpt":"In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen (\"On the number of longest and almost longest cycles in cubic graphs\", Ars Combin., 104, 307--320, 2012) about extremal graphs in these families. In particular, we find families of cyclically $5$-edge connected planar cubic graphs with more Hamilton cycles than the generalized Petersen graphs $P(2n,2)$. The graphs themselves are fullerene graphs that correspond to certain carbon molecules known as nanotubes --- more precisely, the"},"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":"1901.10683","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-30T06:13:41Z","cross_cats_sorted":[],"title_canon_sha256":"79703c63f427b4edc966b6f32b80fde19f90baa3a59d95d98c57fc432ea6964d","abstract_canon_sha256":"3c4363c785056f906603db30633e4fc564bac72bcd4e34ba91887975b811a489"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:02.136438Z","signature_b64":"JRzKXAoToj+7DyBIKG4x09uLE0s540v4fRaYtA/xJn+XD8vhyC0jQnJUro/LaRiS8+/YBwTO0pYmr6al3S1XDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19ecb7f0bcf2e2f03bfde90f112894f0951f384b900d129432e18b5a6e6f2525","last_reissued_at":"2026-05-17T23:54:02.135821Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:02.135821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Highly-connected planar cubic graphs with few or many Hamilton cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gordon Royle, Irene Pivotto","submitted_at":"2019-01-30T06:13:41Z","abstract_excerpt":"In this paper we consider the number of Hamilton cycles in planar cubic graphs of high cyclic edge-connectivity, answering two questions raised by Chia and Thomassen (\"On the number of longest and almost longest cycles in cubic graphs\", Ars Combin., 104, 307--320, 2012) about extremal graphs in these families. In particular, we find families of cyclically $5$-edge connected planar cubic graphs with more Hamilton cycles than the generalized Petersen graphs $P(2n,2)$. The graphs themselves are fullerene graphs that correspond to certain carbon molecules known as nanotubes --- more precisely, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10683","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":"1901.10683","created_at":"2026-05-17T23:54:02.135910+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.10683v2","created_at":"2026-05-17T23:54:02.135910+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10683","created_at":"2026-05-17T23:54:02.135910+00:00"},{"alias_kind":"pith_short_12","alias_value":"DHWLP4F46LRP","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"DHWLP4F46LRPAO75","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"DHWLP4F4","created_at":"2026-05-18T12:33:15.570797+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/DHWLP4F46LRPAO755EHRCKEU6C","json":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C.json","graph_json":"https://pith.science/api/pith-number/DHWLP4F46LRPAO755EHRCKEU6C/graph.json","events_json":"https://pith.science/api/pith-number/DHWLP4F46LRPAO755EHRCKEU6C/events.json","paper":"https://pith.science/paper/DHWLP4F4"},"agent_actions":{"view_html":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C","download_json":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C.json","view_paper":"https://pith.science/paper/DHWLP4F4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.10683&json=true","fetch_graph":"https://pith.science/api/pith-number/DHWLP4F46LRPAO755EHRCKEU6C/graph.json","fetch_events":"https://pith.science/api/pith-number/DHWLP4F46LRPAO755EHRCKEU6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/action/storage_attestation","attest_author":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/action/author_attestation","sign_citation":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/action/citation_signature","submit_replication":"https://pith.science/pith/DHWLP4F46LRPAO755EHRCKEU6C/action/replication_record"}},"created_at":"2026-05-17T23:54:02.135910+00:00","updated_at":"2026-05-17T23:54:02.135910+00:00"}