A Faster Parameterized Algorithm for Pseudoforest Deletion

A pseudoforest is a graph where each connected component contains at most one cycle, or alternatively, a graph that can be turned into a forest by removing at most one edge from each connected component. In this paper, we show that the following problem can be solved in O(3^k n k^{O(1)}) time: given a graph G and an integer k, can we delete at most k vertices from G such that we obtain a pseudoforest? The result improves upon an earlier result by Philip et al. [MFCS 2015] who gave a (nonlinear) 7.56^k n^{O(1)}-time algorithm both in the exponential factor depending on k as well as in the polynomial factor depending on n.