LIPIcs.STACS.2008.1327.pdf
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The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace
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25th International Symposium on Theoretical Aspects of Computer Science (STACS 2008)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2008-02-06
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Thomas Thierauf and Fabian Wagner. The Isomorphism Problem for Planar 3-Connected Graphs is in Unambiguous Logspace. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 633-644, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)
https://doi.org/10.4230/LIPIcs.STACS.2008.1327
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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