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Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width

Authors Narek Bojikian , Stefan Kratsch

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LIPIcs.IPEC.2025.19.pdf
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ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Parameterized complexity
  • connected odd cycle transversal
  • clique-width

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Abstract

Recently, Bojikian and Kratsch [ICALP 2024] presented a novel approach to tackle connectivity problems parameterized by clique-width (cw), based on counting (modulo 2) the number of representations of partial solutions, while allowing for possibly multiple representations to exist for the same partial solution. Using this technique, they got a SETH-tight bound of 𝒪^*(3^{cw}) for the Steiner Tree problem, which was left open by Hegerfeld and Kratsch [ESA 2023]. We use the same technique to solve the Connected Odd Cycle Transversal problem in time 𝒪^*(12^{cw}). Moreover, we prove that our result is tight by providing a SETH-based lower bound excluding algorithms with running time 𝒪^*((12-ε)^{cw}). This answers another question of Hegerfeld and Kratsch [ESA 2023].

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Narek Bojikian and Stefan Kratsch. Tight Bounds for Connected Odd Cycle Transversal Parameterized by Clique-Width. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 19:1-19:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.IPEC.2025.19

Author Details

Narek Bojikian
  • Humboldt-Universität zu Berlin, Germany
Stefan Kratsch
  • Humboldt-Universität zu Berlin, Germany

Acknowledgements

We are grateful to Vera Chekan for her detailed comments on presentation, and to Falko Hegerfeld for several discussions on the lower bound presented here.

References

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