Abstract
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 4 n / n ln ln n ) , 1 − ω ( ln 4 n / n ln ln n ) ] . 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 Bollobás, the random graph isomorphism problem can be solved efficiently for p ∈ [ Θ ( ln n / n ) , 1 − Θ ( ln n / n ) ] .
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