Faster parameterized algorithm for Cluster Vertex Deletion

Abstract

In the Cluster Vertex Deletion problem the input is a 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 the deletion of the vertices of $S$ from $G$ results a graph in which every connected component is a clique. We give an algorithm for Cluster Vertex Deletion whose running time is $O^*(1.811^k)$.