# Faster algorithms for cograph edge modification problems

## TL;DR

This paper presents faster fixed-parameter algorithms for the Cograph Deletion and Cograph Editing problems, improving the efficiency of transforming graphs into cographs by minimizing edge modifications.

## Contribution

The authors develop new algorithms with improved exponential running times for cograph modification problems, advancing the computational methods in graph editing.

## Key findings

- Cograph Deletion algorithm runs in O*(2.303^k) time.
- Cograph Editing algorithm runs in O*(4.329^k) time.
- Algorithms are fixed-parameter tractable with respect to k.

## Abstract

In the Cograph Deletion (resp., Cograph Editing) problem the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of edges of size at most $k$ whose removal from $G$ (resp., removal and addition to $G$) results in a graph that does not contain an induced path with four vertices. In this paper we give algorithms for Cograph Deletion and Cograph Editing whose running times are $O^*(2.303^k)$ and $O^*(4.329^k)$, respectively.