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arXiv · 0707.2522

On embedding well-separable graphs

Béla Csaba
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Abstract

Call 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.

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Béla Csaba. 2007-07-17. On embedding well-separable graphs. https://arxiv.org/abs/0707.2522

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