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A Polynomial Kernel for 3-Leaf Power Deletion

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Jungho Ahn, Eduard Eiben, O-joung Kwon, and Sang-il Oum. A Polynomial Kernel for 3-Leaf Power Deletion. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.MFCS.2020.5

Abstract

For a non-negative integer 𝓁, 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, 3-Leaf Power Deletion 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 treeT. 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^14) vertices.

Subject Classification

ACM Subject Classification
• Theory of computation → Design and analysis of algorithms
• Theory of computation → Graph algorithms analysis
• Theory of computation → Parameterized complexity and exact algorithms
Keywords
• 𝓁-leaf power
• parameterized algorithms
• kernelization

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