Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

TL;DR

This paper introduces a new kernelization technique and an efficient algorithm for the 3-path vertex cover problem, significantly improving the bounds on problem size and computational complexity.

Contribution

It presents the first kernel of size 5k and an O*(1.7485^k)-time algorithm for the parameterized 3-path vertex cover problem, advancing previous bounds.

Findings

Kernel of size 5k vertices established

Algorithm runs in O*(1.7485^k) time

Both results improve upon previous bounds

Abstract

A 3-path vertex cover in a graph is a vertex subset $C$ such that every path of three vertices contains at least one vertex from $C$. The parameterized 3-path vertex cover problem asks whether a graph has a 3-path vertex cover of size at most $k$. In this paper, we give a kernel of $5k$ vertices and an $O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new results improve previous known bounds.