3-connected Planar Graph Isomorphism is in Log-space

Authors Samir Datta, Nutan Limaye, Prajakta Nimbhorkar

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Samir Datta
Nutan Limaye
Prajakta Nimbhorkar

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Samir Datta, Nutan Limaye, and Prajakta Nimbhorkar. 3-connected Planar Graph Isomorphism is in Log-space. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 155-162, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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.
  • Planar graph isomorphism
  • three connected graphs
  • logspace
  • universal exploration sequence


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