Treewidth: Algorithmoc Techniques and Results

We consider a special variant of tree-decompositions, calleddomino tree-decompositions, and the related notion ofdomino treewidth. In a domino tree-decomposition, each vertex of the graph belongs to at most two nodes of the tree. We prove that for ...

We investigate whether an $$n$$n-vertex instance $$(G,k)$$(G,k) of Treewidth, asking whether the graph $$G$$G has treewidth at most $$k$$k, can efficiently be made sparse without changing its answer. By giving a special form of $$\mathop {\mathrm {\...

The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first apply an array of ...