2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142558Turan's theorem implies that every graph of order n with more edges than the r-partite Turan graph contains a complete graph of order r+1. We show that the same premise implies the existence of much larger graphs. We also prove corresponding stability theorems. These results complete work started by Erdos in 1963.Some polishing. Updated referencesCombinatorics05C35text