A note on projective norm graphs
  The projective norm graphs P(q, 4) introduced by Alon, R\'onyai and Szab\'o are explicit examples of extremal graphs not containing K_4,7. Ball and Pepe showed that P(q, 4) does not contain a copy of K_5,5 either for q >= 7, asymptotically improving the best lower bound for ex(n, K_5,5).   We show that these results can not be improved, in the sense that P(q, 4) contains a copy of K_4,6 for infinitely many primes q. 
Codrut Grosu
math.CO math.NT