Planar embeddability of the vertices of a graph using a fixed point set is NP-hard

Let G = (V, E) be a graph with n vertices and let P be a set of n points in the plane. We show that deciding whether there is a planar straight-line embedding of G such that the vertices V are embedded onto the points P is NP-complete, even when G is 2-connected and 2-outerplanar. This settles an open problem posed in [2, 4, 13]. Article Type Communicated by Submitted Revised regular paper M. T. Goodrich July 2005 June 2006 Research done as PhD student at the Institute of Information and Computing Sciences, Utrecht University, The Netherlands. Partially supported by the Cornelis Lely Stichting. 

• Type: Journal
• Year: 2006
• Where: JGAA
• Authors: Sergio Cabello
• Keywords: JGAA 2006, June 2006 Research, Planar Straight-line Embedding, Regular Paper M