{"paper":{"title":"Stable Delaunay Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.CG","authors_text":"Haim Kaplan, Jie Gao, Leonidas J. Guibas, Micha Sharir, Natan Rubin, Pankaj K. Agarwal","submitted_at":"2015-04-26T17:27:02Z","abstract_excerpt":"Let $P$ be a set of $n$ points in $\\mathrm{R}^2$, and let $\\mathrm{DT}(P)$ denote its Euclidean Delaunay triangulation. We introduce the notion of an edge of $\\mathrm{DT}(P)$ being {\\it stable}. Defined in terms of a parameter $\\alpha>0$, a Delaunay edge $pq$ is called $\\alpha$-stable, if the (equal) angles at which $p$ and $q$ see the corresponding Voronoi edge $e_{pq}$ are at least $\\alpha$. A subgraph $G$ of $\\mathrm{DT}(P)$ is called {\\it $(c\\alpha, \\alpha)$-stable Delaunay graph} ($\\mathrm{SDG}$ in short), for some constant $c \\ge 1$, if every edge in $G$ is $\\alpha$-stable and every $c\\a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06851","kind":"arxiv","version":1},"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"}