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 …

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 treedecomposition of G with …

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 find tree-decompositions, …

In this paper we study the complexity of graph decision problems, restricted to the class of
graphs with treewidth ≤k, (or equivalently, the class of partial k-trees), for fixed k. We introduce …

Kernelization is a strong and widely-applied technique in parameterized complexity. A
kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any …

In this paper we consider the following game: players must alternately color the lowest
numbered uncolored vertex of a given graph G= ({1, 2,…, n}, E) with a color, taken from a given …

In this paper we give, for all constantsk,l, explicit algorithms that, given a graphG=(V,E) with
a tree-decomposition ofGwith treewidth at mostl, decide whether the treewidth (or pathwidth) …

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 …

Various parameters of graphs connected to sparse matrix factorization and other applications
can be approximated using an algorithm of Leighton et al. that finds vertex separators of …

We give an algorithm that for an input $n$-vertex graph $G$ and integer $k>0$, in time $2^{O(k)}
n$, either outputs that the treewidth of $G$ is larger than $k$, or gives a tree …