A construction for clique-free pseudorandom graphs

A construction of Alon and Krivelevich gives highly pseudorandom $K_k$-free graphs on $n$ vertices with edge density equal to $Θ(n^{-1/(k -2)})$. 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 $Θ(n^{-1/(k - 1)})$.

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