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.
CITATION STYLE
Aichholzer, O., Aurenhammer, F., Krasser, H., & Hurtado, F. (2001). Towards compatible triangulations. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2108, pp. 101–110). Springer Verlag. https://doi.org/10.1007/3-540-44679-6_12
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