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Sharp Threshold for Hamiltonicity of Random Geometric Graphs

✍ Scribed by Díaz, Josep; Mitsche, Dieter; Pérez, Xavier

Book ID
118196957
Publisher
Society for Industrial and Applied Mathematics
Year
2007
Tongue
English
Weight
154 KB
Volume
21
Category
Article
ISSN
0895-4801

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We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge-length. For fixed k ≥ 1, we prove that the first edge in the process that creates a k-connected graph coincides a.a.s. with