  Let $H$ be a fixed graph. Given a graph $G$ and an integer $k$, the $H$-free
edge modification problem asks whether it is possible to modify at most $k$
edges in $G$ to make it $H$-free. Sandeep and Sivadasan (IPEC 2015) asks
whether the paw-free completion problem and the paw-free edge deletion problem
admit polynomial kernels. We answer both questions affirmatively by presenting,
respectively, $O(k)$-vertex and $O(k^4)$-vertex kernels for them. This is part
of an ongoing program that aims at understanding compressibility of $H$-free
edge modification problems.

Data Structures and Algorithms;Combinatorics