A clique-free pseudorandom subgraph of the pseudo polarity graph

Abstract

We provide a new family of K k -free pseudorandom graphs with edge density Θ(n −1/(k−1) ), matching a recent construction due to Bishnoi, Ihringer and Pepe [BIP20]. As in the former result, the idea is to use large subgraphs of polarity graphs, which are defined over a finite field F q . While their construction required q to be odd, we will give the first construction with q even.