Past exam of the graph Theory and Probabilistic Combinatorics course of the University of Oxford / 2007 / A / 4 / c

For nonempty disjoint vertex sets define $d(X,Y)=e(X,Y)/(|X||Y|)$. The pair is $ϵ$-uniform, also called regular, if whenever $X^{\prime }\subseteq X$ and $Y^{\prime }\subseteq Y$ have sizes at least $ϵ|X|$ and $ϵ|Y|$,Thus reasonably large relative subsets retain almost the same edge density.