Exact Algorithms for Treewidth and Minimum Fill-In - Fomin, Fedor V.; Kratsch, Dieter; Todinca, Ioan; Villanger, Yngve (SIAM journal on computing, 2008)
We show that the treewidth and the minimum fill-in of an $n$-vertex graph can be computed in time $\mathcal{O}(1.8899^n)$. Our results are based on combinatorial proofs that an $n$-vertex graph has $\mathcal{O}(1.7087^n)$ minimal separators and $\mathcal{O}(1.8135^n)$ potential maximal cliques. We also show that for the class of asteroidal triple-free graphs the running time of our algorithms can be reduced to $\mathcal{O}(1.4142^n)$.