Transforming spanning trees and pseudo-triangulations

Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T of TS are adjacent if T intersects T only in points of S or in common edges. We prove that the diameter of TS is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the flip graph PS of pseudo-triangulations of S (where two pseudo-triangulations are adjacent if they differ in exactly one edge

• Type: Journal
• Year: 2006
• Where: IPL
• Authors: Oswin Aichholzer, Franz Aurenhammer, Clemens Huemer, Hannes Krasser
• Keywords: Common Edges, Crossing-free Straight Line, IPL 2006, Planar N-point