# An improved kernel for the cycle contraction problem

## TL;DR

This paper presents an improved kernelization result for the cycle contraction problem, reducing the vertex bound from 6k+6 to 5k+4, advancing the understanding of graph modification problems.

## Contribution

It introduces a tighter kernel for the cycle contraction problem, improving the vertex bound compared to previous work.

## Key findings

- Reduced kernel size from 6k+6 to 5k+4 vertices
- Provides theoretical bounds for graph modification
- Advances parameterized complexity results

## Abstract

The problem of modifying a given graph to satisfy certain properties has been one of the central topics in parameterized tractability study. In this paper, we study the cycle contraction problem, which makes a graph into a cycle by edge contractions. The problem has been studied {by Belmonte et al. [IPEC 2013]} who obtained a linear kernel with at most $6k+6$ vertices. We provide an improved kernel with at most $5k+4$ vertices for it in this paper.