In this paper we consider the flip operation for combinatorial pointed pseudo-triangulations where faces have size 3 or 4, so-called combinatorial 4-PPTs. We show that every combinatorial 4-PPT is stretchable to a geometric pseudo-triangulation, which in general is not the case if faces may have size larger than 4. Moreover, we prove that the flip graph of combinatorial 4-PPTs 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.
- Pub Date:
- October 2013
- Mathematics - Combinatorics;
- Computer Science - Computational Geometry;
- Computer Science - Discrete Mathematics
- 21 pages, 24 figures. Accepted for publication in the special volume of International Journal of Computational Geometry &