# Reducing the domination number of graphs via edge contractions

## TL;DR

This paper investigates the computational complexity of reducing a graph's domination number through a fixed number of edge contractions, providing both positive and negative results.

## Contribution

It introduces the problem of edge contraction to decrease domination number and analyzes its complexity, offering new insights into graph modification problems.

## Key findings

- Complexity results for the edge contraction problem.
- Identification of cases where the problem is tractable.
- Proofs of hardness for certain graph classes.

## Abstract

In this paper, we study the following problem: given a connected graph $G$, can we reduce the domination number of $G$ by at least one using $k$ edge contractions, for some fixed integer $k \geq 0$? We present positive and negative results regarding the computational complexity of this problem.