On Kernels for d-Path Vertex Cover

07/26/2021
by   Radovan Červený, et al.
0

In this paper we study the kernelization of d-Path Vertex Cover (d-PVC) problem. Given a graph G, the problem requires finding whether there exists a set of at most k vertices whose removal from G results in a graph that does not contain a path (not necessarily induced) of length d. It is known that d-PVC is NP-complete for d ≥ 2. Since the problem generalizes to d-Hitting Set, it is known to admit a kernel of size (2d-1)k^d-1+k. We improve on this by giving better kernels. Specifically, we give O(k^2) size (vertices and edges) kernels for the cases when d = 4 and d = 5. Further, we give an O(k^3) size kernel for d-PVC.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

06/21/2019

Faster FPT Algorithm for 5-Path Vertex Cover

The problem of d-Path Vertex Cover, d-PVC lies in determining a subset F...
07/08/2021

Algorithmic aspects of quasi-kernels

In a digraph, a quasi-kernel is a subset of vertices that is independent...
04/26/2018

Who witnesses The Witness? Finding witnesses in The Witness is hard and sometimes impossible

We analyze the computational complexity of the many types of pencil-and-...
12/22/2019

Two novel results on the existence of 3-kernels in digraphs

Let D be a digraph. We call a subset N of V(D)k-independent if for every...
12/07/2018

Kernelization of Packing Problems

Kernelization algorithms are polynomial-time reductions from a problem t...
03/24/2020

Parameterized Algorithms for Red-Blue Weighted Vertex Cover on Trees

Weighted Vertex Cover is a variation of an extensively studied NP-comple...
09/17/2018

Equivalence between pathbreadth and strong pathbreadth

We say that a given graph G = (V, E) has pathbreadth at most ρ, denoted ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.