Abstract

The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace

Thomas Thierauf and Fabian Wagner

Abstract:
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 intersect coUL. As a consequence of our method we get that the isomorphism problem for oriented graphs is in NL. We also show that these problems are hard for logspace.

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