2007/07/24 by Chris Cicotta, Joel Foisy, Cicotta, Chris +9
Computer Science · Mathematics · #05C10 (Secondary) #57M15 (Primary) #57M25 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CO #math.GT #msc:05C10 #msc:57M15 #msc:57M25
paper · pdf · doi:10.48550/arxiv.0707.3615
10 pages, 2 figures
arxiv created 2007/07/24 · openalex publication_date 2007/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A graph G is intrinsically S1-linked if for every embedding of the vertices of G into S1, vertices that form the endpoints of two disjoint edges in G form a non-split link in the embedding. We show that a graph is intrinsically S1-linked if and only if it is not outer-planar. A graph is outer-flat if it can be embedded in the 3-ball such that all of its vertices map to the boundary of the 3-ball, all edges to the interior, and every cycle bounds a disk in the 3-ball that meets the graph only along its boundary. We show that a graph is outer-flat if and only if it is planar.