# Kolmogorov bounds for the normal approximation of the number of triangles in the Erdos-Renyi random graph

## TL;DR

This paper establishes optimal Kolmogorov bounds for the normal approximation of triangle counts in Erdős-Rényi graphs, using a novel Stein-Tikhomirov method, resolving a longstanding open problem.

## Contribution

It provides the first matching Kolmogorov bounds for triangle counts, advancing the understanding of normal approximation in random graphs.

## Key findings

- Bounds match the best Wasserstein bounds from prior work
- Introduces a new Stein-Tikhomirov method variant
- Resolves a long-standing open problem in the field

## Abstract

We bound the error for the normal approximation of the number of triangles in the Erdos-Renyi random graph with respect to the Kolmogorov metric. Our bounds match the best available Wasserstein-bounds obtained by Barbour, Karonski and Rucinski (1989), resolving a long-standing open problem. The proofs are based on a new variant of the Stein-Tikhomirov method - a combination of Stein's method and characteristic functions introduced by Tikhomirov (1980).

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Source: https://tomesphere.com/paper/1704.00410