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

Sergio Cabello
2006 Journal of Graph Algorithms and Applications  
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] .
doi:10.7155/jgaa.00132 fatcat:lz4mc4xlofc2bhtmgy3cjpulmi