A polynomial kernel for 3-leaf power deletion

11/11/2019

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by   Jungho Ahn, et al.

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A graph G is an ℓ-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 ℓ. Given a graph G, the 3-leaf Power Deletion problem asks whether there is a set S⊆ V(G) of size at most k such that G∖ S is a 3-leaf power of some tree T. 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',k') such that k'< k and G' has at most O(k^14log^12k) vertices.