Planar Tree Transformation through Flips

A flip or edge-replacement is considered as a transformation by which one edge e of a geometric object is removed and an edge f (f ne e) is inserted such that the resulting object belongs to the same class as the original object. Here, we consider planar trees as geometric objects. In this paper, we present a technique for transforming a given planar tree into another one for a set S of n points in general position in the plane. We show that any planar tree can be transformed into another planar tree by at most 2n-k-s-2 (0(n)) flips (k > 0 and s > 0 are defined later) which is an improvement of the result in [3].