A Polynomial Kernel for 3-Leaf Power Deletion

For a non-negative integer ?, a graph G is an ?-leaf power of a tree T if V(G) is equal to the set of leaves of T, and distinct vertices v and w of G are adjacent if and only if the distance between v and w in T is at most ?. Given a graph G, 3-Leaf Power Deletion asks whether there is a set S ? V(G) of size at most k such that GS is a 3-leaf power of some treeT. We provide a polynomial kernel for this problem. More specifically, we present a polynomial-time algorithm for an input instance (G,k) to output an equivalent instance (G\u27,k\u27) such that k\u27? k and G\u27 has at most O(k^14) vertices