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Discrete Mathematics & Theoretical Computer Science |
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.
Source : ScholeXplorer
IsRelatedTo ARXIV 1611.09096 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1611.09096
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