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 geome...
| Authors: | , , , , , , , |
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| Format: | article |
| Publication Date: | 2010 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/8079 |
| Online Access: | https://hdl.handle.net/2117/8079 |
| Access Level: | Open access |
| Keyword: | Graph theory Extremal graph theory Geometric graph Perfect matching Spanning tree Grafs, Teoria de Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Summary: | 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. |
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