Document Open Access Logo

Switching Classes: Characterization and Computation

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

PDF
Thumbnail PDF

File

LIPIcs.MFCS.2024.11.pdf
  • Filesize: 0.7 MB
  • 15 pages

Document Identifiers

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.

Cite As Get BibTex

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

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.

Subject Classification

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

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Dhanyamol Antony, Yixin Cao, Sagartanu Pal, and R. B. Sandeep. Switching classes: Characterization and computation, 2024. URL: https://arxiv.org/abs/2403.04263.
  2. Dhanyamol Antony, Jay Garchar, Sagartanu Pal, R. B. Sandeep, Sagnik Sen, and R. Subashini. On subgraph complementation to H-free graphs. Algorithmica, 84(10):2842-2870, 2022. URL: https://doi.org/10.1007/s00453-022-00991-3.
  3. Lowell W Beineke. Characterizations of derived graphs. Journal of Combinatorial theory, 9(2):129-135, 1970. Google Scholar
  4. Hans L. Bodlaender and Jurriaan Hage. On switching classes, NLC-width, cliquewidth and treewidth. Theor. Comput. Sci., 429:30-35, 2012. URL: https://doi.org/10.1016/J.TCS.2011.12.021.
  5. J. Adrian Bondy and F. Mercier. Switching reconstruction of digraphs. J. Graph Theory, 67(4):332-348, 2011. URL: https://doi.org/10.1002/JGT.20535.
  6. Peter J Cameron. Cohomological aspects of two-graphs. Mathematische Zeitschrift, 157:101-119, 1977. Google Scholar
  7. Ying Cheng and Albert L. Wells Jr. Switching classes of directed graphs. J. Comb. Theory, Ser. B, 40(2):169-186, 1986. URL: https://doi.org/10.1016/0095-8956(86)90075-4.
  8. Václáv Chvátal. Set-packing and threshold graphs. Res. Rep., Comput. Sci. Dept., Univ. Waterloo, 1973, 1973. Google Scholar
  9. Charles J. Colbourn and Derek G. Corneil. On deciding switching equivalence of graphs. Discret. Appl. Math., 2(3):181-184, 1980. URL: https://doi.org/10.1016/0166-218X(80)90038-4.
  10. Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk, and Saket Saurabh. Parameterized Algorithms. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21275-3.
  11. Andrzej Ehrenfeucht, Jurriaan Hage, Tero Harju, and Grzegorz Rozenberg. Complexity issues in switching of graphs. In Hartmut Ehrig, Gregor Engels, Hans-Jörg Kreowski, and Grzegorz Rozenberg, editors, Theory and Application of Graph Transformations, 6th International Workshop, TAGT'98, Paderborn, Germany, November 16-20, 1998, Selected Papers, volume 1764 of Lecture Notes in Computer Science, pages 59-70. Springer, 1998. URL: https://doi.org/10.1007/978-3-540-46464-8_5.
  12. Mark N. Ellingham and Gordon F. Royle. Vertex-switching reconstruction of subgraph numbers and triangle-free graphs. J. Comb. Theory, Ser. B, 54(2):167-177, 1992. URL: https://doi.org/10.1016/0095-8956(92)90048-3.
  13. Florent Foucaud, Hervé Hocquard, Dimitri Lajou, Valia Mitsou, and Théo Pierron. Graph modification for edge-coloured and signed graph homomorphism problems: Parameterized and classical complexity. Algorithmica, 84(5):1183-1212, 2022. URL: https://doi.org/10.1007/S00453-021-00918-4.
  14. Jurriaan Hage and Tero Harju. Acyclicity of switching classes. Eur. J. Comb., 19(3):321-327, 1998. URL: https://doi.org/10.1006/EUJC.1997.0191.
  15. Jurriaan Hage and Tero Harju. A characterization of acyclic switching classes of graphs using forbidden subgraphs. SIAM J. Discret. Math., 18(1):159-176, 2004. URL: https://doi.org/10.1137/S0895480100381890.
  16. Jurriaan Hage, Tero Harju, and Emo Welzl. Euler graphs, triangle-free graphs and bipartite graphs in switching classes. Fundam. Informaticae, 58(1):23-37, 2003. URL: http://content.iospress.com/articles/fundamenta-informaticae/fi58-1-03.
  17. Ryan B Hayward. Recognizing p3-structure: A switching approach. journal of combinatorial theory, Series B, 66(2):247-262, 1996. Google Scholar
  18. Alain Hertz. On perfect switching classes. Discret. Appl. Math., 94(1-3):3-7, 1999. URL: https://doi.org/10.1016/S0166-218X(98)00153-X.
  19. Eva Jelínková and Jan Kratochvíl. On switching to H-free graphs. J. Graph Theory, 75(4):387-405, 2014. URL: https://doi.org/10.1002/jgt.21745.
  20. Eva Jelínková, Ondrej Suchý, Petr Hlinený, and Jan Kratochvíl. Parameterized problems related to Seidel’s switching. Discret. Math. Theor. Comput. Sci., 13(2):19-44, 2011. URL: https://doi.org/10.46298/DMTCS.542.
  21. Alexandr V Kostochka. The minimum hadwiger number for graphs with a given mean degree of vertices. Metody Diskret. Analiz., 38:37-58, 1982. Google Scholar
  22. Alexandr V. Kostochka. Lower bound of the hadwiger number of graphs by their average degree. Combinatorica, 4(4):307-316, 1984. Google Scholar
  23. Jan Kratochvíl. Complexity of hypergraph coloring and Seidel’s switching. In Hans L. Bodlaender, editor, Graph-Theoretic Concepts in Computer Science, 29th International Workshop, WG 2003, Elspeet, The Netherlands, June 19-21, 2003, Revised Papers, volume 2880 of Lecture Notes in Computer Science, pages 297-308. Springer, 2003. URL: https://doi.org/10.1007/978-3-540-39890-5_26.
  24. Jan Kratochvíl, Jaroslav Neŝetril, and Ondrej Zỳka. On the computational complexity of Seidel’s switching. In Annals of Discrete Mathematics, volume 51, pages 161-166. Elsevier, 1992. Google Scholar
  25. CL Mallows and NJA Sloane. Two-graphs, switching classes and euler graphs are equal in number. SIAM Journal on Applied Mathematics, 28(4):876-880, 1975. Google Scholar
  26. Suho Oh, Hwanchul Yoo, and Taedong Yun. Rainbow graphs and switching classes. SIAM J. Discret. Math., 27(2):1106-1111, 2013. URL: https://doi.org/10.1137/110855089.
  27. Stephan Olariu. Paw-fee graphs. Inf. Process. Lett., 28(1):53-54, 1988. URL: https://doi.org/10.1016/0020-0190(88)90143-3.
  28. Sang-il Oum. Rank-width and vertex-minors. Journal of Combinatorial Theory, Series B, 95(1):79-100, 2005. URL: https://doi.org/10.1016/J.JCTB.2005.03.003.
  29. Johan Jacob Seidel. Graphs and two-graphs. In Proceedings 5th Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton FL, USA, 1974), pages 125-143, 1974. Google Scholar
  30. Johan Jacob Seidel. A survey of two-graphs. In Atti Convegno Internazionale Teorie Combinatorie (Rome, Italy, September 3-15, 1973), Tomo I., pages 481-511. Accademia Nazionale dei Lincei, 1976. Google Scholar
  31. Johan Jacob Seidel and DE Taylor. Two-graphs, a second survey. In Geometry and Combinatorics, pages 231-254. Elsevier, 1991. Google Scholar
  32. Richard P. Stanley. Reconstruction from vertex-switching. J. Comb. Theory, Ser. B, 38(2):132-138, 1985. URL: https://doi.org/10.1016/0095-8956(85)90078-4.
  33. Andrew Thomason. An extremal function for contractions of graphs. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 95(2), pages 261-265. Cambridge University Press, 1984. Google Scholar
  34. Andrew Thomason. The extremal function for complete minors. J. Comb. Theory, Ser. B, 81(2):318-338, 2001. URL: https://doi.org/10.1006/JCTB.2000.2013.
  35. Jacobus Hendricus van Lint and Johan Jacob Seidel. Equilateral point sets in elliptic geometry. Indagationes Mathematicae, Series A: Mathematical Sciences, 69:335-348, 1966. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact