3-connected Planar Graph Isomorphism is in Log-space

TL;DR

This paper proves that determining whether two 3-connected planar graphs are isomorphic can be done efficiently in deterministic log-space, advancing the computational complexity understanding of this problem.

Contribution

It establishes that 3-connected planar graph isomorphism is solvable within deterministic log-space, improving previous complexity bounds.

Findings

Decidability of 3-connected planar graph isomorphism in log-space.

Improvement over previous UL∩coUL complexity bounds.

Advancement in understanding graph isomorphism complexity.

Abstract

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.