Treewidth of graphs with balanced separations

Treewidth of graphs with balanced separations

We prove that if every subgraph of a graph G has a balanced separation of order at most a then G has treewidth at most 105a. This establishes a linear dependence between the treewidth and the separation number.

On Balanced CSPs with High Treewidth

Tractable cases of the binary CSP are mainly divided in two classes: constraint language restrictions and constraint graph restrictions. To better understand and identify the hardest binary CSPs, in this work we propose methods to increase their hardness by increasing the balance of both the constraint language and the constraint graph. The balance of a constraint is increased by maximizing the...

Treewidth of Circle Graphs

In this paper we show that the treewidth of a circle graph can be computed in polynomial time. A circle graph is a graph that is isomorphic to the intersection graph of a finite collection of chords of a circle. The TREEWIDTH problem can be viewed upon as the problem of finding a chordal embedding of the graph that minimizes the maximum clique size. Our algorithm to determine the treewidth of a...

Treewidth of Line Graphs

We determine the exact treewidth of the line graph of the complete graph. More generally, we determine the exact treewidth of the line graph of a regular complete multipartite graph. For an arbitrary complete multipartite graph, we determine the treewidth of the line graph up to a lower order term.

Treewidth of planar graphs: connections with duality