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A Polynomial Kernel for Deletion to the Scattered Class of Cliques and Trees

Authors Ashwin Jacob , Diptapriyo Majumdar , Meirav Zehavi

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Author Details

Ashwin Jacob
  • National Institute of Technology Calicut, Kozhikode, India
Diptapriyo Majumdar
  • Indraprastha Institute of Information Technology Delhi, New Delhi, India
Meirav Zehavi
  • Ben-Gurion University of The Negev, Beersheba, Israel

Funding

  • Majumdar, Diptapriyo: Supported by Science and Engineering Research Board (SERB) grant SRG/2023/001592.
  • Zehavi, Meirav: Supported by European Research Council (ERC) starting grant titled PARAPATH.

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Ashwin Jacob, Diptapriyo Majumdar, and Meirav Zehavi. A Polynomial Kernel for Deletion to the Scattered Class of Cliques and Trees. In 35th International Symposium on Algorithms and Computation (ISAAC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 322, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ISAAC.2024.41

Abstract

The class of graph deletion problems has been extensively studied in theoretical computer science, particularly in the field of parameterized complexity. Recently, a new notion of graph deletion problems was introduced, called deletion to scattered graph classes, where after deletion, each connected component of the graph should belong to at least one of the given graph classes. While fixed-parameter algorithms were given for a wide variety of problems, little progress has been made on the kernelization complexity of any of them. Here, we present the first non-trivial polynomial kernel for one such deletion problem, where, after deletion, each connected component should be a clique or a tree - that is, as dense as possible or as sparse as possible (while being connected). We develop a kernel of O(k⁵) vertices for the same.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized Complexity
  • Kernelization
  • Scattered Graph Classes
  • New Expansion Lemma
  • Cliques or Trees Vertex Deletion

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