On random points in the unit disk

Let n be a positive integer and > 0 a real number. Let Vn be a set of n points in the unit disk selected uniformly and independently at random. Define G(, n) to be the graph with vertex set Vn, in which two vertices are adjacent if and only if their Euclidean distance is at most . We call this graph a unit disk random graph. Let = c ln n/n and let X be the number of isolated points in G(, n). We prove that almost always X n1-c2

• Type: Journal
• Year: 2006
• Where: RSA
• Authors: Robert B. Ellis, Xingde Jia, Catherine H. Yan
• Keywords: Positive Integer, Real Number, RSA 2006, Unit Disk