{"paper":{"title":"Angle-Monotone Graphs: Construction and Local Routing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anna Lubiw, Debajyoti Mondal","submitted_at":"2018-01-19T04:26:18Z","abstract_excerpt":"A geometric graph in the plane is angle-monotone of width $\\gamma$ if every pair of vertices is connected by an angle-monotone path of width $\\gamma$, a path such that the angles of any two edges in the path differ by at most $\\gamma$. Angle-monotone graphs have good spanning properties.\n  We prove that every point set in the plane admits an angle-monotone graph of width $90^\\circ$, hence with spanning ratio $\\sqrt 2$, and a subquadratic number of edges. This answers an open question posed by Dehkordi, Frati and Gudmundsson.\n  We show how to construct, for any point set of size $n$ and any ang"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06290","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"}