The connectivity of a graph on uniform points on [0,\,1]\(^{d}\).

DOI10.1016/S0167-7152(02)00233-XzbMath1039.05054OpenAlexW1996807175MaRDI QIDQ1871346

Martin J. B. Appel, Ralph P. Russo

Publication date: 7 May 2003

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-7152(02)00233-x

zbMATH Keywords

geometric probability

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Combinatorial probability (60C05) Connectivity (05C40)

Related Items (8)

Unnamed Item ⋮ One-dimensional geometric random graphs with nonvanishing densities. II: A very strong zero-one law for connectivity ⋮ Thresholds for vanishing of `isolated' faces in random Čech and Vietoris-Rips complexes ⋮ The connectivity threshold of random geometric graphs with Cantor distributed vertices ⋮ Monotone properties of random geometric graphs have sharp thresholds ⋮ Thresholding random geometric graph properties motivated by ad hoc sensor networks ⋮ Plane and planarity thresholds for random geometric graphs ⋮ A New Random Graph Model with Self-Optimizing Nodes: Connectivity and Diameter

Cites Work

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• A log log law for maximal uniform spacings
• The longest edge of the random minimal spanning tree
• A strong law for the longest edge of the minimal spanning tree
• Boundary domination and the distribution of the largest nearest-neighbor link in higher dimensions
• The Maximum Vertex Degree of a Graph on Uniform Points in [0, 1^d]
• The Minimum Vertex Degree of a Graph on Uniform Points in [0, 1^d]
• The limit distribution of the largest nearest-neighbour link in the unit d-cube

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