Augmenting the connectivity of geometric graphs

Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, 2n 3 additional edges are required in some cases and that 6n 7 additional edges are always sufficient. For the special case of plane geometric trees, these bounds decrease to n 2 and 2n 3 , respectively.

• Type: Journal
• Year: 2008
• Where: COMGEO
• Authors: Manuel Abellanas, Alfredo García Olaverri, Ferran Hurtado, Javier Tejel, Jorge Urrutia
• Keywords: Additional Edges, Applied Computing, COMGEO 2008, Connected Plane, Plane Geometric Graphs