A Polynomial Kernel for 3-Leaf Power Deletion

Jungho Ahn, Eduard Eiben, O-joung Kwon, Sang-il Oum

Abstract: For a non-negative integer \(\ell \), the \(\ell \)-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 \(\ell \). 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 \(k'\leqslant k\) and \(G'\) has at most \(O(k^{14})\) vertices.