FPT algorithms for generalized feedback vertex set problems

TL;DR

This paper investigates the fixed-parameter tractability of deleting the minimum number of vertices to transform a graph into an r-pseudoforest or a d-quasi-forest, generalizing the feedback vertex set problem.

Contribution

It introduces improved FPT algorithms and kernelization results for r-pseudoforest deletion and establishes FPT results for d-quasi-forest deletion.

Findings

Enhanced FPT algorithms for r-pseudoforest deletion

Kernelization results for r-pseudoforest deletion

FPT algorithms for d-quasi-forest deletion

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.