= Logarithmic Erdős-Stone theorem
{title2=$t\ge\lfloor d(r,\epsilon)\log n\rfloor$}
= Erdős-Stone-Bollobás theorem
{c}
{synonym}
An <edge> density exceeding the <Turan theorem> threshold for $K_{r+1}$ by a fixed positive amount forces a balanced $K_{r+1}(t)$ subgraph with logarithmic part size. Combine <clique supersaturation by sampling> with the <dense clique family blow-up lemma>. Dense binomial random <graphs> show that the logarithmic order is optimal for a uniform density guarantee.
Back to article page
