2 problems

For $\varepsilon>0$, a graph $G$ is $(N,\varepsilon)$-restricted if its vertex set can be partitioned into at most $N$ subsets that are $\varepsilon$-restricted in $G$, where a sub…

Let $G$ be a graph, let $H$ be a graph, and let $\rho(H,G)=\operatorname{ind}_H(G)/\abs{G}^{\abs H}$. For every $\varepsilon>0$, consider the parameters $\delta$ and $\kappa$ in Ni…