FPT Algorithms for Generalized Feedback Vertex Set Problems

Abstract

An r-pseudoforest is a graph in which each component can be made into a forest by deleting at most r edges, and a d-quasi-forest is a graph in which each component can be made into a forest by deleting at most d vertices. In this paper, we study the parameterized tractability of deleting minimum number of vertices to obtain r-pseudoforest and d-quasi-forest, generalizing the well-studied feedback vertex set problem. We first provide improved FPT algorithm and kernelization results for the r-pseudoforest deletion problem, and then we show that the d-quasi-forest deletion problem is also FPT.