Polynomial kernels for paw-free edge modification problems

Abstract

Given a graph G and an integer k, the paw-free completion problem asks whether it is possible to add at most k edges to G to make it paw-free. The paw-free edge deletion problem is defined analogously. Sandeep and Sivadasan (IPEC 2015) asked whether these problems admit polynomial kernels. We answer both questions affirmatively by presenting, respectively, O(k)-vertex and O(k4)-vertex kernels for them. This is part of an ongoing program that aims at understanding the compressibility of H-free edge modification problems for general H.