On the Number of Pseudo-Triangulations of Certain Point Sets

We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically \(12^n n^{\Theta(1)}\) pointed pseudo-triangulations, which lies...

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Bibliographic Details
Published inarXiv.org
Main Authors Oswin Aichholzer, Orden, David, Santos, Francisco, Speckmann, Bettina
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.06.2007
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Summary:We pose a monotonicity conjecture on the number of pseudo-triangulations of any planar point set, and check it on two prominent families of point sets, namely the so-called double circle and double chain. The latter has asymptotically \(12^n n^{\Theta(1)}\) pointed pseudo-triangulations, which lies significantly above the maximum number of triangulations in a planar point set known so far.
ISSN:2331-8422
DOI:10.48550/arxiv.0601747