Improved random graph isomorphism

Canonical labeling of a graph consists of assigning a unique label to each vertex such that the labels are invariant under isomorphism. Such a labeling can be used to solve the graph isomorphism problem. We give a simple, linear time, high probability algorithm for the canonical labeling of a G(n, p) random graph for p ∈ [ ω ( ln n/n ln lnn ) , 1− ω ( ln n/n ln lnn )] . Our result covers a gap in the range of p in which no algorithm was known to work with high probability. Together with a previous result by Bollobas, the random graph isomorphism problem can be solved efficiently for p ∈ [Θ (lnn/n) , 1−Θ(lnn/n)].