Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
On compatible triangulations of simple polygons
Computational Geometry: Theory and Applications
Enumerating order types for small sets with applications
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
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We state the following conjecture: any two planar n-point sets (that agree on the number of convex hull points) can be triangulated in a compatible manner, i.e., such that the resulting two planar graphs are isomorphic. The conjecture is proved true for point sets with at most three interior points. We further exhibit a class of point sets which can be triangulated compatibly with any other set (that satisfies the obvious size and hull restrictions). Finally, we prove that adding a small number of Steiner points (the number of interior points minus two) always allows for compatible triangulations.