A polynomial kernel for $3$-leaf power deletion

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

doi:10.1007/s00453-023-01129-9

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arXiv · 1911.04249

A polynomial kernel for $3$-leaf power deletion

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

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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 $k'\leq k$ and $G'$ has at most $O(k^{14})$ vertices.

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Jungho Ahn, Eduard Eiben, O-joung Kwon, Sang-il Oum. 2023-10-23. A polynomial kernel for $3$-leaf power deletion. https://doi.org/10.1007/s00453-023-01129-9

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