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URN: urn:nbn:de:0030-drops-17491
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### 3-connected Planar Graph Isomorphism is in Log-space

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### Abstract

We consider the isomorphism and canonization problem for \$3\$-connected planar graphs. The problem was known to be \Log-hard and in \ULcoUL\ \cite{TW07}. In this paper, we give a deterministic log-space algorithm for \$3\$-connected planar graph isomorphism and canonization. This gives an \Log-completeness result, thereby settling its complexity. \par The algorithm uses the notion of universal exploration sequences from \cite{koucky01} and \cite{Rei05}. To our knowledge, this is a completely new approach to graph canonization.

### BibTeX - Entry

```@InProceedings{datta_et_al:LIPIcs:2008:1749,
author =	{Samir Datta and Nutan Limaye and Prajakta Nimbhorkar},
title =	{{3-connected Planar Graph Isomorphism is in Log-space}},
booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages =	{155--162},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-08-8},
ISSN =	{1868-8969},
year =	{2008},
volume =	{2},
editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address =	{Dagstuhl, Germany},
URL =		{http://drops.dagstuhl.de/opus/volltexte/2008/1749},
URN =		{urn:nbn:de:0030-drops-17491},
doi =		{http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2008.1749},
annote =	{Keywords: Planar graph isomorphism, three connected graphs, logspace, universal exploration sequence}
}
```

 Keywords: Planar graph isomorphism, three connected graphs, logspace, universal exploration sequence Seminar: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science Related Scholarly Article: Issue date: 2008 Date of publication: 2008

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