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arXiv:2604.22365 · v2

Dynamic Planar Graph Isomorphism is in DynFO

Samir DattaAsif KhanFelix TschirbsNils VortmeierThomas Zeume
cs.LOcs.CC
首次提交 2026-04-24 16:56
版本更新 2026-10-26 18:53
雷达观测 2026-10-29 00:36
arXiv ↗PDF ↗

摘要

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.

作者备注：Full version of a LICS 2026 paper

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v2 · 2026-10-26 18:53 · 最新观测版本

Dynamic Planar Graph Isomorphism is in DynFO

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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