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Switching Classes: Characterization and Computation

Authors Dhanyamol Antony , Yixin Cao , Sagartanu Pal, R. B. Sandeep

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Switching
  • Graph modification
  • Minor-closed graph class
  • Hereditary graph class

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Abstract

In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class 𝒢, we are concerned with the maximum subclass and the minimum superclass of 𝒢 that are closed under switching. We characterize the maximum subclass for many important classes 𝒢, and prove that it is finite when 𝒢 is minor-closed and omits at least one graph. For several graph classes, we develop polynomial-time algorithms to recognize the minimum superclass. We also show that the recognition of the superclass is NP-hard for H-free graphs when H is a sufficiently long path or cycle, and it cannot be solved in subexponential time assuming the Exponential Time Hypothesis.

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Dhanyamol Antony, Yixin Cao, Sagartanu Pal, and R. B. Sandeep. Switching Classes: Characterization and Computation. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.11

Author Details

Dhanyamol Antony
  • Department of Computer Science and Automation, Indian Institute of Science, Bengaluru, India
Yixin Cao
  • Department of Computing, Hong Kong Polytechnic University, Hong Kong, China
Sagartanu Pal
  • Department of Computer Science & Engineering, Indian Institute of Technology Dharwad, India
R. B. Sandeep
  • Department of Computer Science & Engineering, Indian Institute of Technology Dharwad, India

Funding

Supported by SERB grants CRG/2022/006770 and MTR/2022/000692, RGC grant 15221420, and NSFC grants 61972330 and 62372394.

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