Treewidth reduction for constrained separation and bipartization problems

TL;DR

This paper introduces a treewidth reduction technique that preserves minimal s-t separators, enabling fixed-parameter tractability proofs for various constrained separation and bipartization problems, thus advancing parameterized complexity theory.

Contribution

The paper presents a novel treewidth reduction method that facilitates fixed-parameter tractability results for several constrained graph separation problems.

Findings

Proves fixed-parameter tractability of constrained separation problems.

Introduces a treewidth reduction technique preserving minimal s-t separators.

Answers open questions in parameterized complexity.

Abstract

We present a method for reducing the treewidth of a graph while preserving all the minimal $s-t$ separators. This technique turns out to be very useful for establishing the fixed-parameter tractability of constrained separation and bipartization problems. To demonstrate the power of this technique, we prove the fixed-parameter tractability of a number of well-known separation and bipartization problems with various additional restrictions (e.g., the vertices being removed from the graph form an independent set). These results answer a number of open questions in the area of parameterized complexity.