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Dynamic Planar Graph Isomorphism Is in DynFO

Authors Samir Datta , Asif Khan , Felix Tschirbs , Nils Vortmeier , Thomas Zeume

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LIPIcs.LICS.2026.36.pdf
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ACM Subject Classification
  • Theory of computation → Complexity theory and logic
Keywords
  • Dynamic complexity theory
  • parallel computation
  • dynamic algorithms

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Abstract

Consider two planar graphs which are subject to edge insertions and deletions. We show that whether the two graphs are isomorphic can be maintained with first-order logic formulas and auxiliary data of polynomial size. This places the dynamic planar graph isomorphism problem into the dynamic descriptive complexity class DynFO. As a consequence, there is a dynamic constant-time parallel algorithm with polynomial-size auxiliary data which maintains whether two dynamic planar graphs are isomorphic.

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Samir Datta, Asif Khan, Felix Tschirbs, Nils Vortmeier, and Thomas Zeume. Dynamic Planar Graph Isomorphism Is in DynFO. In 41st Annual Symposium on Logic in Computer Science (LICS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 380, pp. 36:1-36:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.LICS.2026.36

Author Details

Samir Datta
  • Chennai Mathematical Institute & UMI ReLaX, Chennai, India
Asif Khan
  • Chennai Mathematical Institute, India
Felix Tschirbs
  • Ruhr University Bochum, Germany
Nils Vortmeier
  • Ruhr University Bochum, Germany
Thomas Zeume
  • Ruhr University Bochum, Germany

Funding

Samir Datta and Asif Khan are partially funded by a grant from Infosys foundation. Felix Tschirbs, Nils Vortmeier and Thomas Zeume are supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant 532727578.

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