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Reconfiguring Independent Sets on Interval Graphs

Authors Marcin Briański, Stefan Felsner, Jędrzej Hodor, Piotr Micek

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • reconfiguration
  • independent sets
  • interval graphs

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Abstract

We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size k are reconfigurable in an n-vertex interval graph, then there is a reconfiguration sequence of length 𝒪(k⋅ n²). We also provide a construction in which the shortest reconfiguration sequence is of length Ω(k²⋅ n).
As a counterpart to these results, we also establish that Independent Set Reconfiguration is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.

Cite As Get BibTex

Marcin Briański, Stefan Felsner, Jędrzej Hodor, and Piotr Micek. Reconfiguring Independent Sets on Interval Graphs. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 23:1-23:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.MFCS.2021.23

Author Details

Marcin Briański
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Stefan Felsner
  • Institut für Mathematik, Technische Universität Berlin, Germany
Jędrzej Hodor
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Piotr Micek
  • Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

Funding

M. Briański, J. Hodor, P. Micek are partially supported by a Polish National Science Center grant (BEETHOVEN; UMO-2018/31/G/ST1/03718).

References

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