Computing the Treewidth and the Minimum Fill-In with the Modular Decomposition

@article{Bodlaender2002ComputingTT,
  title={Computing the Treewidth and the Minimum Fill-In with the Modular Decomposition},
  author={Hans L. Bodlaender and Udi Rotics},
  journal={Algorithmica},
  year={2002},
  volume={36},
  pages={375-408}
}
Using the notion of modular decomposition we extend the class of graphs on which both the treewidth and the minimum fill-in can be solved in polynomial time. We show that if C is a class of graphs that are modularly decomposable into graphs that have a polynomial number of minimal separators, or graphs formed by adding a matching between two cliques, then both the treewidth and the minimum fill-in on C can be solved in polynomial time. For the graphs that are modular decomposable into cycles we… CONTINUE READING