Edge-Removal and Non-Crossing Configurations in Geometric Graphs

Oswin Aichholzer, Sergio Cabello, Ruy Fabila-Monroy, David Flores-Peñaloza, Thomas Hackl, Clemens Huemer, Ferran Hurtado, David R. Wood
2010 Discrete Mathematics & Theoretical Computer Science  
Graphs and Algorithms International audience 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 non-crossing subgraphs that we consider are
more » ... rfect matchings, subtrees of a given size, and triangulations. In each case, we obtain tight bounds on the maximum number of removable edges.
doi:10.46298/dmtcs.525 fatcat:2aevw6sqrbbm5bs6rxxmd5yveq