Treewidth computation and extremal combinatorics

@article{Fomin2008TreewidthCA,
  title={Treewidth computation and extremal combinatorics},
  author={F. Fomin and Yngve Villanger},
  journal={Combinatorica},
  year={2008},
  volume={32},
  pages={289-308}
}
AbstractFor a given graph G and integers b,f ≥0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most $n\left( {_b^{b + f} } \right)$ such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several enumeration and exact algorithms. In particular, we use it to provide… 
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