Treewidth and Minimum Fill-in of Weakly Triangulated Graphs

We use the notion of potential maximal clique to characterize the maximal cliques appearing in minimal triangulations of a graph. We show that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum fill-in are polynomially tractable for these graphs. Finally we show how to compute in polynomial time the potential maximal cliques of weakly triangulated graphs.

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