Faster FPT Algorithms for Deletion to Pairs of Graph Classes

Abstract

Let \(\varPi \) be a hereditary graph class. The problem of deletion to \(\varPi \), takes as input a graph G and asks for a minimum number (or a fixed integer k) of vertices to be deleted from G so that the resulting graph belongs to \(\varPi \). This is a well-studied problem in paradigms including approximation and parameterized complexity. This problem, for example, generalizes vertex cover, feedback vertex set, cluster vertex deletion, perfect deletion to name a few. The study of this problem in parameterized complexity has resulted in several powerful algorithmic techniques including iterative compression and important separators.