H. Bodlaender, "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1998), pp. 1-45.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for this paper. Keywords: Tree decompositions, treewidth, disjoint rooted paths. 1. Introduction The notions of tree decompositions and treewidth of a graph were introduced in the 1980 s by Robertson and Seymour [17] and they have since found a large number of applications (see Bodlaender [12] for a tutorial on graph treewidth and its applications) We shall define tree decompositions and treewidth precisely in the next section. For now it will suffice to think of a tree decomposition of a graph G as a decomposition of the vertex set of G into pieces that fit together in a tree like ....

....in linear time. In fact, given a tree decomposition of G of constant width, one can solve in linear time any optimization problem on G that can be expressed in monadic second order logic. Furthermore, other problems such as graph isomorphism can be solved in polynomial time (for references see [12]) This is what spurred an interest in finding tree decompositions of small (constant) width in graphs which have them. The first algorithm for finding an O(k) tree decomposition (for some constant k) was due to Robertson and Seymour [17] and had an O(n f(k) running time on graphs with n ....

H. L. Bodlaender, "A partial k-arboretum of graphs with bounded treewidth," Theoret. Comput. Sci. 209:1-2 (1998) 1--45

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H. Bodlaender, "A partial k-arboretum of graphs with bounded treewidth", Theoretical Computer Science, 209 (1998), pp. 1-45.

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