An O^*(2.619^k) algorithm for 4-path vertex cover

TL;DR

This paper introduces a parameterized algorithm for the 4-path vertex cover problem with a time complexity of O^*(2.619^k), improving the efficiency of solving this problem in graphs.

Contribution

The paper presents the first fixed-parameter algorithm for 4-path vertex cover with a runtime of O^*(2.619^k), advancing algorithmic techniques for this problem.

Findings

Achieved a new algorithm with O^*(2.619^k) complexity

Improved the computational approach for 4-path vertex cover

Provides a foundation for further parameterized algorithms

Abstract

In the 4-path vertex cover problem, the input is an undirected graph $G$ and an integer $k$. The goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every path with 4 vertices in $G$ contains at least one vertex of $S$. In this paper we give a parameterized algorithm for 4-path vertex cover whose time complexity is $O^*(2.619^k)$.