On embedding well-separable graphs

Call a simple graph H of order nwell-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 @c>0 and positive integer @D there exists an n"0 such that if n>n"0, @D(H)= =(1-1/2(@g(H)-1)[email protected])n for a simple graph G of order n, then [email protected]?G. We extend our result to graphs with small band-width, too.

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