Random Graph Isomorphism

@article{Babai1980RandomGI,
  title={Random Graph Isomorphism},
  author={L{\'a}szl{\'o} Babai and Paul Erd{\"o}s and Stanley M. Selkow},
  journal={SIAM J. Comput.},
  year={1980},
  volume={9},
  pages={628-635}
}
A straightforward linear time canonical labeling algorithm is shown to apply to almost all graphs (i.e. all but $o(2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} )$) of the $2^{( \begin{subarray}{l} n \\ 2 \end{subarray} )} $ graphs on n vertices). Hence, for almost all graphs X, any graph Y can be easily tested for isomorphism to X by an extremely naive linear time algorithm. This result is based on the following: In almost all graphs on n vertices, the largest $n^{0.15} $ degrees are… 
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