A note on projective norm graphs

Abstract

The projective norm graphs [Formula: see text] introduced by Alon, Rónyai and Szabó are explicit examples of extremal graphs not containing [Formula: see text]. Ball and Pepe showed that [Formula: see text] does not contain a copy of [Formula: see text] either for [Formula: see text], asymptotically improving the best lower bound for [Formula: see text]. We show that these results cannot be improved, in the sense that [Formula: see text] contains a copy of [Formula: see text] for infinitely many primes [Formula: see text].