3-connected Planar Graph Isomorphism is in Log-space

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.

• Type: Conference
• Year: 2008
• Where: FSTTCS
• Authors: Samir Datta, Nutan Limaye, Prajakta Nimbhorkar
• Keywords: 3-connected Planar Graph, Canonization Problem, FSTTCS 2008, Planar Graph Isomorphism, Software Engineering