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The Length of the Shortest Edge of a Graph on a Sphere

✍ Scribed by Hiroshi Maehara

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 62 KB
Volume: 23
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2002.0598

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✦ Synopsis

Let S d denote a unit sphere in the (d + 1)-dimensional Euclidean space R d+1 (d ≥ 1). For a simple graph G E with edge set E, take independent random points x k , k ∈ V (G E ), on S d , and let D E be the minimum value of the spherical distance between x i , x j for {i, j} ∈ E. We prove that

, where B( p, q) is the beta function.

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