Edge-Removal and Non-Crossing Configurations in Geometric Graphs
Rights accessOpen Access
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 perfect matchings, subtrees of a given size, and triangulations. In each case, we obtain tight bounds on the maximum number of removable edges.
CitationAichholzer, O. [et al.]. Edge-Removal and Non-Crossing Configurations in Geometric Graphs. "Discrete mathematics and theoretical computer science", 2010, vol. 12, núm. 1, p. 75-86.