Dynamic Planar Graph Isomorphism is in DynFO
Logic in Computer Science
2026-04-27 v1 Computational Complexity
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.
Cite
@article{arxiv.2604.22365,
title = {Dynamic Planar Graph Isomorphism is in DynFO},
author = {Samir Datta and Asif Khan and Felix Tschirbs and Nils Vortmeier and Thomas Zeume},
journal= {arXiv preprint arXiv:2604.22365},
year = {2026}
}
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Full version of a LICS 2026 paper