FLIPS IN COMBINATORIAL POINTED PSEUDO-TRIANGULATIONS WITH FACE DEGREE AT MOST FOUR

Abstract

In this paper we consider the ip operation for combinatorial pointed pseudotriangulations 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 ip graph of combinatorial 4-PPTs is connected and has diameter O(n2), even in the case of labeled vertices with fixed outer face. For this case we provide an Ω(n log n) lower bound.