Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices

• DOI: 10.1007/s00454-009-9149-3
• Publication Date: 2009-02-25T19:42:48Z
• Authors: Hazel Everett; Sylvain Lazard; Giuseppe Liotta; Stephen Wismath
• Keywords: Computational geometry; universal point sets; simultaneous embeddings; [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG]; 0102 computer and information sciences; [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG]; 01 natural sciences

This paper shows that any planar graph with $n$ vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this result is that any number of planar graphs admit a simultaneous embedding without mapping with at most one bend per edge.