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DOI: 10.4230/LIPIcs.MFCS.2024.11

Switching Classes: Characterization and Computation

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

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

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)

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@InProceedings{antony_et_al:LIPIcs.MFCS.2024.11,
  author =	{Antony, Dhanyamol and Cao, Yixin and Pal, Sagartanu and Sandeep, R. B.},
  title =	{{Switching Classes: Characterization and Computation}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.11},
  URN =		{urn:nbn:de:0030-drops-205678},
  doi =		{10.4230/LIPIcs.MFCS.2024.11},
  annote =	{Keywords: Switching, Graph modification, Minor-closed graph class, Hereditary graph class}
}

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Switching Classes: Characterization and Computation

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