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For a graph G, let Π(G) denote the set of all potential maximal cliques of G. For each subset Π of Π(G), let (G, Π) denote the smallest k such that there is a tree-decomposition of G of width k whose bags all belong to Π. Bouchitté and Todinca observed in 2001 that (G, Π(G)) is exactly the treewidth of G and developed a dynamic programming algorithm to compute it. Indeed, their algorithm can readily be applied to an arbitrary non-empty subset Π of Π(G) and computes (G, Π), or reports that it isarXiv:1909.07647v2 fatcat:r7nj7vtzljemfnecsehvw6q3ya