@misc{gdea_3599, editor = {J\'anos Pach}, title = {The Three Dimensional Logic Engine}, author = {Matthew Kitching and Sue Whitesides}, publisher = {Springer}, year = {2004}, pages = {329--339}, url = {http://gdea.informatik.uni-koeln.de/599/}, abstract = {We consider the following graph embedding question: given a graph G, is it possible to map its vertices to points in 3D such that G is isomorphic to the mutual nearest neighbor graph of the set P of points to which the vertices are mapped? We show that this problem is NP-hard. We do this by extending the "logic engine" method to three dimensions by using building blocks inpired by the structure of diamond and by constructions of A.G. Bell and B. Fuller.} }