Graham triangulations and triangulations with a center are hamiltonean
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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 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.
[1] Michael Ian Shamos,et al. Computational geometry: an introduction , 1985 .
[2] Ronald L. Graham,et al. An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..
[3] Reuven Bar-Yehuda,et al. Time/space tradeoffs for polygon mesh rendering , 1996, TOGS.
[4] Steven Skiena,et al. Hamiltonian triangulations for fast rendering , 1996, The Visual Computer.
[5] Prosenjit Bose,et al. No Quadrangulation is Extremely Odd , 1995, ISAAC.