# Faster parameterized algorithm for pumpkin vertex deletion set

## TL;DR

This paper presents an efficient fixed-parameter algorithm with exponential time complexity for the pumpkin vertex deletion set problem, which involves removing vertices to transform a directed graph into a pumpkin structure.

## Contribution

The paper introduces a new $O^*(2^k)$ time algorithm for deciding whether a directed graph can be converted into a pumpkin by deleting at most $k$ vertices, improving computational efficiency.

## Key findings

- Algorithm runs in $O^*(2^k)$ time.
- Decides pumpkin vertex deletion set with fixed-parameter tractability.
- Provides a practical approach for graph modification problems.

## Abstract

A directed graph $G$ is called a pumpkin if $G$ is a union of induced paths with a common start vertex $s$ and a common end vertex $t$, and the internal vertices of every two paths are disjoint. We give an algorithm that given a directed graph $G$ and an integer $k$, decides whether a pumpkin can be obtained from $G$ by deleting at most $k$ vertices. The algorithm runs in $O^*(2^k)$ time.