Sub-Gaussian Tails for the Number of Triangles in G( n, p)

Let X be the random variable that counts the number of triangles in the binomial random graph G(n, p). We show that for some positive constant c, the probability that X deviates from its expectation by at least λ Var(X)1/2 is at most e−cλ2 , provided p = o(1), λ = ω( √ ln n) and λ ≤ (n3 p3 + n4 p5 )1/6 .

• Type: Journal
• Year: 2011
• Where: CPC
• Authors: Guy Wolfovitz
• Keywords: Binomial Random Graph, CPC 2011, Education, Random Variable, Triangles