# A construction for clique-free pseudorandom graphs

## TL;DR

This paper improves a known construction of pseudorandom graphs that avoid complete subgraphs, achieving higher edge density while maintaining pseudorandom properties, thus advancing the understanding of extremal graph configurations.

## Contribution

It introduces a new construction method that produces an infinite family of denser, highly pseudorandom, $K_k$-free graphs compared to previous results.

## Key findings

- Achieves higher edge density in $K_k$-free pseudorandom graphs
- Provides an explicit construction for an infinite family of such graphs
- Enhances the theoretical bounds on pseudorandom graph density

## Abstract

A construction of Alon and Krivelevich gives highly pseudorandom $K_k$-free graphs on $n$ vertices with edge density equal to $\Theta(n^{-1/(k -2)})$. In this short note we improve their result by constructing an infinite family of highly pseudorandom $K_k$-free graphs with a higher edge density of $\Theta(n^{-1/(k - 1)})$.