Polynomial kernels for 3-leaf power graph modification problems

Abstract

A graph G = (V,E) is a 3-leaf power iff there exists a tree T the leaf set of which is V and such that (u, v) ∈ E iff u and v are at distance at most 3 in T. The 3-leaf power edge modification problems, i.e. edition (also known as the Closest 3-Leaf Power), completion and edge-deletion are FPT when parameterized by the size of the edge set modification. However, a polynomial kernel was known for none of these three problems. For each of them, we provide a kernel with O(k3) vertices that can be computed in linear time. We thereby answer an open question first mentioned by Dom, Guo, Hüffner and Niedermeier [9]. © Springer-Verlag Berlin Heidelberg 2009.