3-connected Planar Graph Isomorphism is in Log-space

Samir Datta, Nutan Limaye & Prajakta Nimbhorkar
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.