Flips in combinatorial pointed pseudotriangulations with face degree at most four
Abstract
In this paper we consider the flip operation for combinatorial pointed pseudotriangulations where faces have size 3 or 4, socalled combinatorial 4PPTs. We show that every combinatorial 4PPT is stretchable to a geometric pseudotriangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the flip graph of combinatorial 4PPTs is connected and has diameter $O(n^2)$, even in the case of labeled vertices with fixed outer face. For this case we provide an $\Omega(n\log n)$ lower bound.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.0833
 Bibcode:
 2013arXiv1310.0833A
 Keywords:

 Mathematics  Combinatorics;
 Computer Science  Computational Geometry;
 Computer Science  Discrete Mathematics
 EPrint:
 21 pages, 24 figures. Accepted for publication in the special volume of International Journal of Computational Geometry &