{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JI7XRYKJIIZGDMRP22DBB4G4DU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8982f0318d617ad36bd84028ea9002200a730596e18ce7b7dd5f17f0801d28a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-11-08T14:53:44Z","title_canon_sha256":"59f57490ae3206b7483b317a15be6385dce4d26d9a43b94d9dd86b4d5527d684"},"schema_version":"1.0","source":{"id":"1611.02541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.02541","created_at":"2026-05-18T00:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1611.02541v2","created_at":"2026-05-18T00:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.02541","created_at":"2026-05-18T00:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"JI7XRYKJIIZG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JI7XRYKJIIZGDMRP","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JI7XRYKJ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:6c5743f584aa48bd63a03d74d44bf63f9778ba28e93e3de9ae7ee4a342db5edf","target":"graph","created_at":"2026-05-18T00:59:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We show that every triangulation (maximal planar graph) on $n\\ge 6$ vertices can be flipped into a Hamiltonian triangulation using a sequence of less than $n/2$ combinatorial edge flips. The previously best upper bound uses $4$-connectivity as a means to establish Hamiltonicity. But in general about $3n/5$ flips are necessary to reach a $4$-connected triangulation. Our result improves the upper bound on the diameter of the flip graph of combinatorial triangulations on $n$ vertices from $5.2n-33.6$ to $5n-23$. We also show that for every triangulation on $n$ vertices there is a simultaneous fli","authors_text":"Csaba D. T\\'oth, Jean Cardinal, Manuel Wettstein, Michael Hoffmann, Vincent Kusters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-11-08T14:53:44Z","title":"Arc diagrams, flip distances, and Hamiltonian triangulations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02541","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4f893aeb4046d469f3cd9c0dd1750161257578d4998d0d373653ddd5bbeda9ad","target":"record","created_at":"2026-05-18T00:59:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8982f0318d617ad36bd84028ea9002200a730596e18ce7b7dd5f17f0801d28a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2016-11-08T14:53:44Z","title_canon_sha256":"59f57490ae3206b7483b317a15be6385dce4d26d9a43b94d9dd86b4d5527d684"},"schema_version":"1.0","source":{"id":"1611.02541","kind":"arxiv","version":2}},"canonical_sha256":"4a3f78e149423261b22fd68610f0dc1d226ddc9b2ab33e877119bbb0a96c26fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a3f78e149423261b22fd68610f0dc1d226ddc9b2ab33e877119bbb0a96c26fc","first_computed_at":"2026-05-18T00:59:34.023239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:34.023239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pIQtdu8+aeoC0WYCinHcAk+5UqM/kQIQf20W4qv85ufMJkjOAMJYoo2eWglyzO7QrnjRNgTbk5BJo4fx+lauBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:34.023904Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.02541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f893aeb4046d469f3cd9c0dd1750161257578d4998d0d373653ddd5bbeda9ad","sha256:6c5743f584aa48bd63a03d74d44bf63f9778ba28e93e3de9ae7ee4a342db5edf"],"state_sha256":"e0aaded37500b094f816a68ebea770c10ac3cb7888cf44f9693c867c9ba0cea5"}