{"paper":{"title":"Strong convexity in flip-graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Lionel Pournin, Zili Wang","submitted_at":"2021-06-15T09:46:13Z","abstract_excerpt":"The triangulations of a surface $\\Sigma$ with a prescribed set of vertices can be endowed with a graph structure $\\mathcal{F}(\\Sigma)$. Its edges connect two triangulations that differ by a single arc. It is known that, when $\\Sigma$ is a convex polygon or a topological surface, the subgraph $\\mathcal{F}_\\varepsilon(\\Sigma)$ induced in $\\mathcal{F}(\\Sigma)$ by the triangulations that contain a given arc $\\varepsilon$ is strongly convex in the sense that all the geodesic paths between two such triangulations remain in that subgraph. Here, we provide a related result that involves a triangle ins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.08012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.08012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}