{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:RNLIHAOV4TRDWM5AHRXJKG4XSH","short_pith_number":"pith:RNLIHAOV","schema_version":"1.0","canonical_sha256":"8b568381d5e4e23b33a03c6e951b9791d3bd88acb00bac02c2563e9cae4fda4f","source":{"kind":"arxiv","id":"1110.6473","version":2},"attestation_state":"computed","paper":{"title":"Making triangulations 4-connected using flips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andr\\'e van Renssen, Dana Jansens, Maria Saumell, Prosenjit Bose, Sander Verdonschot","submitted_at":"2011-10-28T21:48:49Z","abstract_excerpt":"We show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter "},"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":"1110.6473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2011-10-28T21:48:49Z","cross_cats_sorted":[],"title_canon_sha256":"17d53772403eb21ebe83362cfd26c7104bc5a1fa3b7146c561caf422fa6ab195","abstract_canon_sha256":"fa0d20144bf42d464adaa5081ad30b262f0735a0a489315deb286ee88c8bad19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.482035Z","signature_b64":"+rhSXxfuPaXbzl8NS4l7LS6EX2ItnpR2K56HZ/rqvg02lCPsV3G9VwYF9RKIC3IvK+8a+Wr8iVAxtkBS3YxkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b568381d5e4e23b33a03c6e951b9791d3bd88acb00bac02c2563e9cae4fda4f","last_reissued_at":"2026-05-18T01:33:49.481506Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.481506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Making triangulations 4-connected using flips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Andr\\'e van Renssen, Dana Jansens, Maria Saumell, Prosenjit Bose, Sander Verdonschot","submitted_at":"2011-10-28T21:48:49Z","abstract_excerpt":"We show that any combinatorial triangulation on n vertices can be transformed into a 4-connected one using at most floor((3n - 9)/5) edge flips. We also give an example of an infinite family of triangulations that requires this many flips to be made 4-connected, showing that our bound is tight. In addition, for n >= 19, we improve the upper bound on the number of flips required to transform any 4-connected triangulation into the canonical triangulation (the triangulation with two dominant vertices), matching the known lower bound of 2n - 15. Our results imply a new upper bound on the diameter "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6473","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":"1110.6473","created_at":"2026-05-18T01:33:49.481582+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.6473v2","created_at":"2026-05-18T01:33:49.481582+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6473","created_at":"2026-05-18T01:33:49.481582+00:00"},{"alias_kind":"pith_short_12","alias_value":"RNLIHAOV4TRD","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"RNLIHAOV4TRDWM5A","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"RNLIHAOV","created_at":"2026-05-18T12:26:41.206345+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/RNLIHAOV4TRDWM5AHRXJKG4XSH","json":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH.json","graph_json":"https://pith.science/api/pith-number/RNLIHAOV4TRDWM5AHRXJKG4XSH/graph.json","events_json":"https://pith.science/api/pith-number/RNLIHAOV4TRDWM5AHRXJKG4XSH/events.json","paper":"https://pith.science/paper/RNLIHAOV"},"agent_actions":{"view_html":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH","download_json":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH.json","view_paper":"https://pith.science/paper/RNLIHAOV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.6473&json=true","fetch_graph":"https://pith.science/api/pith-number/RNLIHAOV4TRDWM5AHRXJKG4XSH/graph.json","fetch_events":"https://pith.science/api/pith-number/RNLIHAOV4TRDWM5AHRXJKG4XSH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH/action/storage_attestation","attest_author":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH/action/author_attestation","sign_citation":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH/action/citation_signature","submit_replication":"https://pith.science/pith/RNLIHAOV4TRDWM5AHRXJKG4XSH/action/replication_record"}},"created_at":"2026-05-18T01:33:49.481582+00:00","updated_at":"2026-05-18T01:33:49.481582+00:00"}