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

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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∩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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Authors and Affiliations

  1. Fak. Elektronik und Informatik, HTW Aalen, 73430, Aalen, Germany

    Thomas Thierauf

  2. Inst. für Theoretische Informatik, Universität Ulm, 89069, Ulm, Germany

    Fabian Wagner

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  1. Thomas Thierauf
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  2. Fabian Wagner
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Correspondence to Thomas Thierauf.

Additional information

Supported by DFG grants Scho 302/7-2 and TO 200/2-2.

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Thierauf, T., Wagner, F. The Isomorphism Problem for Planar 3-Connected Graphs Is in Unambiguous Logspace. Theory Comput Syst 47, 655–673 (2010). https://doi.org/10.1007/s00224-009-9188-4

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  • DOI: https://doi.org/10.1007/s00224-009-9188-4

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