Planar embeddability of the vertices of a graph using a fixed point set is NP-hard Vol. 10, no. 2, pp. 353-363, 2006. Regular paper. Abstract 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 [,,]. Submitted: July 2005. Revised: June 2006. Communicated by Michael T. Goodrich article (PDF) BibTeX