Edge-Removal and Non-Crossing Configurations in Geometric Graphs

A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . We study the following extremal problem for geometric graphs: How many arbitrary edges can be removed from a complete geometric graph with n vertices such that the remaining graph still contains a certain non-crossing subgraph. The noncrossing subgraphs that we consider are perfect matchings, subtrees of a given size, and triangulations. In each case, we obtain tight bounds on the maximum number of removable edges.

• Type: Journal
• Year: 2010
• Where: DMTCS
• Authors: Oswin Aichholzer, Sergio Cabello, Ruy Fabila Monroy, David Flores-Peñaloza, Thomas Hackl, Clemens Huemer, Ferran Hurtado, David R. Wood
• Keywords: Certain Non-crossing Subgraph, Complete Geometric Graph, DMTCS 2010, Geometric Graph, Sensor Networks