An Improved FPT Algorithm and Quadratic Kernel for Pathwidth One Vertex Deletion

Abstract

The Pathwidth One Vertex Deletion (POVD) problem, given an undirected graph G and an integer k, asks whether one can delete at most k vertices from G so that the remaining graph has pathwidth at most 1. Recently Philip et al.[14] initiated the study of the parameterized complexity of (POVD) and have shown a quartic kernel and a 7 k n O(1) algorithm. In this paper we improve these results by showing a quadratic kernel and a 4.65 k n O(1) algorithm.