# 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}
}
• Published 9 March 2008
• Mathematics
• Combinatorica
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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