3-connected Planar Graph Isomorphism is in Log-space

Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Marc Herbstritt
2008 Foundations of Software Technology and Theoretical Computer Science  
We consider the isomorphism and canonization problem for 3-connected planar graphs. The problem was known to be L -hard and in UL ∩ coUL [TW08]. In this paper, we give a deterministic log-space algorithm for 3-connected planar graph isomorphism and canonization. This gives an L -completeness result, thereby settling its complexity. The algorithm uses the notion of universal exploration sequences from [Kou02] and [Rei05]. To our knowledge, this is a completely new approach to graph canonization.
doi:10.4230/lipics.fsttcs.2008.1749 dblp:conf/fsttcs/DattaLN08 fatcat:kiwbi4xxgjg6jateoetglsmpbi