# Approximating Max-Cut under Graph-MSO Constraints

## TL;DR

This paper presents a $rac{1}{2}$-approximation algorithm for max-cut and max-$k$-cut problems with graph constraints expressible in MSO logic on graphs of constant treewidth, expanding the scope of solvable constrained max-cut problems.

## Contribution

The paper introduces a novel approximation algorithm for constrained max-cut problems on graphs with MSO-expressible constraints and bounded treewidth, broadening previous methods.

## Key findings

- Achieves a 1/2 approximation ratio for the problem.
- Handles any MSO-expressible constraints on graphs of constant treewidth.
- Extends the applicability of max-cut algorithms to more complex graph constraints.

## Abstract

We consider the max-cut and max-$k$-cut problems under graph-based constraints. Our approach can handle any constraint specified using monadic second-order (MSO) logic on graphs of constant treewidth. We give a $\frac{1}{2}$-approximation algorithm for this class of problems.