TITLE: Complexity of graph isomorphism
QUESTION [7 upvotes]: Last year, Laszlo Babai proved that the graph isomorphism problem can be solved in time:
$$ \exp(O(\log^c n)) $$
where $n$ is the number of vertices.
What is the best bound we have for $c$? (The case $c = 1$ would correspond to a polynomial-time algorithm for graph isomorphism.)

REPLY [4 votes]: Babai apparently retracted some parts of his proof, now he claims that he can do $O(\exp(n^c))$ for some small $c$ (say, $c=0.01$), but not all $c>0$. See http://people.cs.uchicago.edu/~laci/update.html