# A Constraint Model for the Tree Decomposition of a Graph

## TL;DR

This paper introduces a constraint-based approach for generating tree decompositions of graphs, enabling the determination of tree width and providing explicit decompositions as proof.

## Contribution

It presents a novel constraint model that simultaneously computes the tree width and constructs a corresponding tree decomposition.

## Key findings

- Successfully computes tree width for various graphs
- Provides explicit tree decompositions as witnesses
- Demonstrates effectiveness of constraint programming in graph decomposition

## Abstract

We present a constraint model for the problem of producing a tree decomposition of a graph. The inputs to the model are a simple graph G, the number of nodes in the desired tree decomposition and the maximum cardinality of each node in that decomposition. Via a sequence of decision problems, the model allows us to find the tree width of a graph whilst delivering a tree decomposition of that width, i.e. a witness.