On Tuza’s conjecture for triangulations and graphs with small treewidth

Treewidth for Graphs with Small Chordality

A graph G is k-chordal, if it does not contain chordless cycles of length larger than k. The chordality Ic of a graph G is the minimum k for which G is k-chordal. The degeneracy or the width of a graph is the maximum min-degree of any of its subgraphs. Our results are the following: ( 1) The problem of treewidth remains NP-complete when restricted to graphs with small maximum degree. (2) An upp...

NC-Algorithms for Graphs with Small Treewidth

On Reduction Algorithms for Graphs with Small Treewidth

Some new ideas are presented on graph reduction applied to graphs with bounded treewidth. It is shown that the method can not only be applied to solve decision problems, but also some optimization problems and construction variants of several of these problems on graphs with some constant upper bound on the treewidth. Also, the exisitence is shown of nite, safe, complete, and terminating sets o...

Reduction Algorithms for Graphs of Small Treewidth

This paper presents a number of new ideas and results on graph reduction applied to graphs of bounded treewidth. Arnborg et al. [2] have shown that many decision problems on graphs can be solved in linear time on graphs of bounded treewidth, by using a finite set of reduction rules. These algorithms can be used to solve problems on graphs of bounded treewidth without the need to first obtain a ...

Dynamic Programming on Graphs with Bounded Treewidth