Faster parameterized algorithm for r-pseudoforest deletion

Abstract

In the r-Pseudoforest Deletion problem, the input is a graph G and integers $k,r$, and the goal is to decide whether there is a set of at most k vertices whose removal from G results in a graph in which every connected component can be made into a tree by deleting at most r edges. In this paper we give an $O^{⁎}\left({(8r+1)}^k\right)$-time algorithm for r-Pseudoforest Deletion for every $r\ge 1$.