A Polynomial Kernel for 3-Leaf Power Deletion

For a non-negative integer ℓ , the ℓ - leaf power of a tree T is a simple graph G on the leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most ℓ . We provide a polynomial kernel for the problem of deciding whether we can delete at most k vertices to make an input graph a 3-leaf power of some tree. More specifically, we present a polynomial-time algorithm for an input instance ( G , k ) for the problem to output an equivalent instance (G',k') such that k'⩽ k and G' has at most O(k^14) vertices.