A $5k$-vertex Kernel for $P_2$-packing

TL;DR

This paper presents a new kernelization algorithm for the P2-packing problem, reducing any instance to a graph with at most 5k vertices, improving the efficiency of solving this problem.

Contribution

It introduces a novel 5k-vertex kernel for P2-packing, advancing the kernelization techniques for this problem.

Findings

Developed a 5k-vertex kernel for P2-packing.

Improved the theoretical bounds for kernel size.

Contributed to the understanding of kernelization in graph problems.

Abstract

The $P_2$-packing problem asks for whether a graph contains $k$ vertex-disjoint paths each of length two. We continue the study of its kernelization algorithms, and develop a $5k$-vertex kernel.