# 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}
}
• Published 1 August 1980
• Mathematics
• SIAM J. Comput.
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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