Graham triangulations and triangulations with a center are hamiltonean

Let P be a point set with n elements in general position. A triangulation T of P is a set of triangles with disjoint interiors such that their union is the convex hull of P , no triangle contains an element of P in in its interior, and the vertices of the triangles of T are points of P . Given T we define a graph G(T ) whose vertices are the triangles of T , two of which are adjacent if they share an edge. We say that T is hamiltonean if G(T ) has a hamiltonean path. We prove that the triangulations produced by Graham’s Scan are hamiltonean. Furthermore we prove that any triangulation T of a point set which has a point adjacent to all the points in P (a center of T ) is hamiltonean.