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.
Cite
@article{arxiv.1912.06966,
title = {FPT algorithms for generalized feedback vertex set problems},
author = {Bin Sheng},
journal= {arXiv preprint arXiv:1912.06966},
year = {2019}
}