2013/10/18 by Tarik Aougab, Samuel J. Taylor · 13 citations
Computer Science · Mathematics · #Botany #Combinatorics #Computational Geometry and Mesh Generation #Discrete mathematics #Genus #Geodesic #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Graph #Intersection (aeronautics) #Intersection graph #Line graph #Mathematics #math.GT
paper · pdf · doi:10.1112/blms/bdu057
published in Bulletin of the London Mathematical Society 46(5), 989-1002 (Wiley) · 13 pages, 6 figures
arxiv created 2013/10/18 · openalex publication_date 2014/07/15 · arxiv updated 2017/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Let S g , p denote the genus g orientable surface with p ⩾ 0 punctures, and let ω ( g , p ) = 3 g + p − 3 > 1 . We prove the existence of infinitely long geodesic rays ( v 0 , v 1 , v 2 , … ) in the curve graph satisfying the following optimal intersection property: for any natural numbers i and k, the endpoints v i , v i + k of any length k subsegment intersect at most f i , k ( ω ) times, where f i , k ( x ) is O ( x k − 2 ) . This answers a question of Dan Margalit.