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A Polynomial Kernel for 3-Leaf Power Deletion

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

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Notes

  1. A class of graphs is non-trivial if both itself and its complement contain infinitely many non-isomorphic graphs.

  2. A class of graphs is hereditary if it is closed under taking induced subgraphs.

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Funding

This article was funded by Institute for Basic Science under Grant No. (IBS-R029-C1) and National Research Foundation of Korea under Grant No. (NRF-2018R1D1A1B07050294).

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Authors and Affiliations

  1. Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea

    Jungho Ahn, O.-joung Kwon & Sang-il Oum

  2. Department of Mathematical Sciences, KAIST, Daejeon, South Korea

    Jungho Ahn & Sang-il Oum

  3. Department of Computer Science, Royal Holloway, University of London, Egham, UK

    Eduard Eiben

  4. Department of Mathematics, Hanyang University, Seoul, South Korea

    O.-joung Kwon

Authors
  1. Jungho Ahn
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  2. Eduard Eiben
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  4. Sang-il Oum
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Correspondence to Jungho Ahn.

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An extended abstract appeared in the Proceedings of the 45th international symposium on mathematical foundations of computer science [4].

Supported by the Institute for Basic Science (IBS-R029-C1).

Supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (Nos. NRF-2018R1D1A1B07050294 and NRF-2021K2A9A2A11101617).

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Ahn, J., Eiben, E., Kwon, Oj. et al. A Polynomial Kernel for 3-Leaf Power Deletion. Algorithmica 85, 3058–3087 (2023). https://doi.org/10.1007/s00453-023-01129-9

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  • DOI: https://doi.org/10.1007/s00453-023-01129-9

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