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Reducing CMSO to Unbreakable Graphs Cannot Be Computable

Authors Colin Geniet , Roohani Sharma

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Theory of computation → Computability
  • Theory of computation → Logic
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Unbreakability
  • CMSO
  • Uncomputability
  • Meta-theorem

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Abstract

Lokshtanov, Ramanujan, Saurabh, and Zehavi [ICALP 2018] proved that for any CMSO formula ϕ, testing ϕ on arbitrary graphs can be reduced to testing it on (q,k)-unbreakable graphs for appropriate parameters. Their proof is non-constructive, and they ask whether it can be made constructive. We prove that this is impossible: specifically, the parameter q cannot be a computable function of ϕ.

Cite As Get BibTex

Colin Geniet and Roohani Sharma. Reducing CMSO to Unbreakable Graphs Cannot Be Computable. In 34th Annual European Symposium on Algorithms (ESA 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 388, pp. 91:1-91:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.ESA.2026.91

Author Details

Colin Geniet
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea
Roohani Sharma
  • Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, South Korea

Funding

  • Geniet, Colin: Supported by the Institute for Basic Science (IBS-R029-C1).
  • Sharma, Roohani: Supported by the Young Scientist Fellowship (YSF) of the Institute for Basic Science (IBS-R029-Y8).

References

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