2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134548Call a simple graph $H$ of order $n$ well-separable, if by deleting a separator set of size $o(n)$ the leftover will have components of size at most $o(n)$. We prove, that bounded degree well-separable spanning subgraphs are easy to embed: for every $γ>0$ and positive integer $Δ$ there exists an $n_0$ such that if $n>n_0$, $Δ(H) \le Δ$ for a well-separable graph $H$ of order $n$ and $δ(G) \ge (1-{1 \over 2(χ(H)-1)} + γ)n$ for a simple graph $G$ of order $n$, then $H \subset G$. We extend our result to graphs with small band-width, too.11 pages, submitted for publicationCombinatorics05C35text