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arXiv · 0802.2825

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

Thomas Thierauf·Fabian Wagner
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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 $AC^1$. In this paper we improve the upper bound for planar 3-connected graphs to unambiguous logspace, in fact to $UL \cap coUL$. 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 $L$.

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Thomas Thierauf, Fabian Wagner. 2008-02-20. The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace. https://arxiv.org/abs/0802.2825

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