Planar Graph Isomorphism is in Log-Space

Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Thomas Thierauf, Fabian Wagner
2022 ACM Transactions on Computation Theory  
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. The gap between the known upper and lower bounds continues to be very significant for many subclasses of graphs as well. We bridge the gap for a natural and important class of graphs, namely planar graphs, by presenting a log-space upper bound which matches the known log-space hardness. In fact, we show a stronger result that planar graph canonization is in log-space.
doi:10.1145/3543686 fatcat:glhtpo6suzgztpmihwy4xew5le