In this paper, we give for constant k a linear-time algorithm that, given a graph G (V, E), determines whether the treewidth of G is at most k and, if so, finds a tree-decomposition of G withâ€¦ (More)

Kernelization is a strong and widely-applied technique in parameterized complexity. In a nutshell, a kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transformsâ€¦ (More)

The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies. This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniformâ€¦ (More)

Abstract. We present an algorithm that constructively produces a solution to the k -DOMINATING SET problem for planar graphs in time O(c^ \sqrt k n) , where c=4^ 6\sqrt 34 . To obtain this result, weâ€¦ (More)

In this paper we give, for all constants k, l, explicit algorithms, that given a graph G = (V, E) with a tree-decomposition of G with treewidth at most l, decide whether the treewidth (or pathwidth)â€¦ (More)

A short overview is given of many recent results in algorithmic graph theory that deal with the notions treewidth, and pathwidth. We discuss algorithms that nd tree-decompositions, algorithms thatâ€¦ (More)

This paper gives an overview of several results and techniques for graphs algorithms that compute the treewidth of a graph or that solve otherwise intractable problems when restricted graphs withâ€¦ (More)

32 that a canonical ordering or a 4-connected triangular planar graph is possible, in which every vertex v k has out(v k) 2, which decreases the width of a visibility representation by a factor 2.â€¦ (More)