For more and more applications, it is important to be able to compute the treewidth of a given
graph and to find tree decompositions of small width reasonably fast. This paper gives an …

This paper is a review which presents and explains the decomposition of graphs by clique
minimal separators. The pace is leisurely, we give many examples and figures. Easy …

Treewidth is a graph parameter with several interesting theoretical and practical
applications. This survey reviews algorithmic results on determining the treewidth of a given …

Any given graph can be embedded in a chordal graph by adding edges, and the resulting
chordal graph is called a triangulation of the input graph. In this paper we study minimal …

We continue the study of (tw, ω)-bounded graph classes, that is, hereditary graph classes in
which the treewidth can only be large due to the presence of a large clique, with the goal of …

The Minimum Fill-in problem is used to decide if a graph can be triangulated by adding at
most k edges. In 1994, Kaplan, Shamir, and Tarjan showed that the problem is solvable in …

This chapter gives a general overview of two emerging techniques for discrete optimization
that have footholds in mathematics, computer science, and operations research: branch …

We give a novel general approach for solving NP-hard optimization problems that combines
dynamic programming and fast matrix multiplication. The technique is based on reducing …

This thesis consists of two parts. In the second part the research papers that constitute the
new results of the thesis are presented. In this first part we want to put these results in a …

We present an algorithm with runtime O (k (2k) n3* m) for the following NP-complete
problem: Given an arbitrary graph G on n vertices and m edges, can we obtain an interval …