Thomas Thierauf and Fabian Wagner
The isomorphism problem for planar graphs is known to be efficiently solvable.
For planar 3-connected graphs,
the isomorphism problem can be solved by efficient parallel algorithms,
it is in the class AC1.
In this paper
we improve the upper bound for planar 3-connected graphs to unambiguous logspace,
in fact to UL ∩ coUL.
As a consequence of our method we get that the isomorphism problem for oriented graphs is in NL.
We also show that the problems are hard for L.