Augmenting the Edge Connectivity of Planar Straight Line Graphs to Three

We characterize the planar straight line graphs (Pslgs) that can be augmented to 3‐connected and 3‐edge‐connected Pslgs, respectively. We show that if a Pslg with n vertices can be augmented to a 3‐edge‐connected Pslg, then at most 2n−2 new edges are always sufficient and sometimes necessary for the augmentation. If the input Pslg is, in addition, already 2‐edge‐connected, then n−2 new edges are always sufficient and sometimes necessary for the augmentation to a 3‐edge‐connected Pslg.