arXiv - CS - Discrete Mathematics Pub Date : 2019-11-11 , DOI: arxiv-1911.04249
Jungho Ahn; Eduard Eiben; O-joung Kwon; Sang-il Oum

A graph $G$ is an $\ell$-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 $\ell$. Given a graph $G$, the $3$-Leaf Power Deletion problem asks whether there is a set $S\subseteq V(G)$ of size at most $k$ such that $G\setminus S$ 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 $k'\leq k$ and $G'$ has at most $O(k^{14})$ vertices.

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