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Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number

Authors Maria Chudnovsky , Jadwiga Czyżewska , Kacper Kluk , Marcin Pilipczuk , Paweł Rzążewski

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
Keywords
  • P_t-free graphs
  • maximum weight induced subgraph
  • maximum weight independent set

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Abstract

Many natural computational problems, including e.g. Max Weight Independent Set, Feedback Vertex Set, or Vertex Planarization, can be unified under an umbrella of finding the largest sparse induced subgraph that satisfies some property definable in CMSO₂ logic. It is believed that each problem expressible with this formalism can be solved in polynomial time in graphs that exclude a fixed path as an induced subgraph. This belief is supported by the existence of a quasipolynomial-time algorithm by Gartland, Lokshtanov, Pilipczuk, Pilipczuk, and Rzążewski [STOC 2021], and a recent polynomial-time algorithm for P₆-free graphs by Chudnovsky, McCarty, Pilipczuk, Pilipczuk, and Rzążewski [SODA 2024].
In this work we extend polynomial-time tractability of all such problems to P₇-free graphs of bounded clique number.

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Maria Chudnovsky, Jadwiga Czyżewska, Kacper Kluk, Marcin Pilipczuk, and Paweł Rzążewski. Sparse Induced Subgraphs in P₇-Free Graphs of Bounded Clique Number. In 36th International Symposium on Algorithms and Computation (ISAAC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 359, pp. 20:1-20:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ISAAC.2025.20

Author Details

Maria Chudnovsky
  • Princeton University, NJ, USA
Jadwiga Czyżewska
  • University of Warsaw, Poland
Kacper Kluk
  • University of Warsaw, Poland
Marcin Pilipczuk
  • University of Warsaw, Poland
Paweł Rzążewski
  • Warsaw University of Technology, Poland
  • University of Warsaw, Poland

Funding

  • Chudnovsky, Maria: Supported by NSF Grant DMS-2348219 and by AFOSR grant FA9550-22-1-0083.
  • Czyżewska, Jadwiga: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143.
  • Kluk, Kacper: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143.
  • Pilipczuk, Marcin: Supported by Polish National Science Centre SONATA BIS-12 grant number 2022/46/E/ST6/00143.
  • Rzążewski, Paweł: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreement number 948057.

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