We show that the isomorphism of 3-connected planar graphs can be decided in
deterministic log-space. This improves the previously known bound UL$\cap$coUL
of Thierauf and Wagner

Datta, Samir

Limaye, Nutan

Nimbhorkar, Prajakta

English

arXiv

We consider the isomorphism and canonization
problem for $3$-connected planar graphs. The
problem was known to be Log-hard and in ULcoUL cite{TW07}. In this
paper, we give a deterministic log-space algorithm for $3$-connected
planar graph isomorphism and canonization. 
This gives an Log-completeness result,
thereby settling its complexity.
par The algorithm uses the notion of universal exploration sequences
from cite{koucky01} and cite{Rei05}. To our knowledge, this is a
completely new approach to graph canonization

3-connected Planar Graph Isomorphism is in Log-space

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