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2015 A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphs
Xiao Fang
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Electron. Commun. Probab. 20: 1-6 (2015). DOI: 10.1214/ECP.v20-3707

Abstract

Let $\{G_n: n\geq 1\}$ be a sequence of simple graphs. Suppose $G_n$ has $m_n$ edges and each vertex of $G_n$ is colored independently and uniformly at random with $c_n$ colors. Recently, Bhattacharya, Diaconis and Mukherjee (2013) proved universal limit theorems for the number of monochromatic edges in $G_n$. Their proof was by the method of moments, and therefore was not able to produce rates of convergence. By a non-trivial application of Stein's method, we prove that there exists a universal error bound for their central limit theorem. The error bound depends only on $m_n$ and $c_n$, regardless of the graph structure.

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Xiao Fang. "A universal error bound in the CLT for counting monochromatic edges in uniformly colored graphs." Electron. Commun. Probab. 20 1 - 6, 2015. https://doi.org/10.1214/ECP.v20-3707

Information

Accepted: 5 March 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1320.05039
MathSciNet: MR3320409
Digital Object Identifier: 10.1214/ECP.v20-3707

Subjects:
Primary: 05C15
Secondary: 60F05

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