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QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes

Authors Édouard Bonnet , Jadwiga Czyżewska , Tomáš Masařík , Marcin Pilipczuk , Paweł Rzążewski

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Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • independent set
  • long holes
  • QPTAS
  • induced subgraphs

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Abstract

We present a quasipolynomial-time approximation scheme (QPTAS) for the Maximum Independent Set (MWIS) in graphs with a bounded number of pairwise vertex-disjoint and non-adjacent long induced cycles. More formally, for every fixed s and t, we show a QPTAS for MWIS in graphs that exclude sC_t as an induced minor. Combining this with known results, we obtain a QPTAS for the problem of finding a largest induced subgraph of bounded treewidth with given hereditary property definable in Counting Monadic Second Order Logic, in the same classes of graphs.
This is a step towards a conjecture of Gartland and Lokshtanov which asserts that for any planar graph H, graphs that exclude H as an induced minor admit a polynomial-time algorithm for the latter problem. This conjecture is notoriously open and even its weaker variants are confirmed only for very restricted graphs H.

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Édouard Bonnet, Jadwiga Czyżewska, Tomáš Masařík, Marcin Pilipczuk, and Paweł Rzążewski. QPTAS for MWIS and Finding Large Sparse Induced Subgraphs in Graphs with Few Independent Long Holes. In 20th Scandinavian Symposium on Algorithm Theory (SWAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 370, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SWAT.2026.9

Author Details

Édouard Bonnet
  • Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
Jadwiga Czyżewska
  • University of Warsaw, Poland
Tomáš Masařík
  • University of Warsaw, Poland
Marcin Pilipczuk
  • University of Warsaw, Poland
Paweł Rzążewski
  • Warsaw University of Technology, Poland
  • University of Warsaw, Poland

Funding

  • Czyżewska, Jadwiga: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143.
  • Masařík, Tomáš: Supported by the Polish National Science Centre SONATA-17 grant number 2021/43/D/ST6/03312.
  • Pilipczuk, Marcin: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143.
  • Rzążewski, Paweł: Supported by the National Science Centre grant 2024/54/E/ST6/00094.

Acknowledgements

The project was initiated at the Structural Graph Theory workshop STWOR in September 2023. This workshop was a part of STRUG: Structural Graph Theory Bootcamp, funded by the "Excellence initiative - research university (2020-2026)" of University of Warsaw. We are grateful to Benjamin Bergougnoux, Linda Cook, and Marek Sokołowski for stimulating discussions on the topic.

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