{"paper":{"title":"There are Plane Spanners of Maximum Degree 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Ge Xia, Iyad Kanj, Ljubomir Perkovi\\'c, Nicolas Bonichon","submitted_at":"2014-03-21T02:50:05Z","abstract_excerpt":"Let E be the complete Euclidean graph on a set of points embedded in the plane. Given a constant t >= 1, a spanning subgraph G of E is said to be a t-spanner, or simply a spanner, if for any pair of vertices u,v in E the distance between u and v in G is at most t times their distance in E. A spanner is plane if its edges do not cross.\n  This paper considers the question: \"What is the smallest maximum degree that can always be achieved for a plane spanner of E?\" Without the planarity constraint, it is known that the answer is 3 which is thus the best known lower bound on the degree of any plane"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5350","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"}