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Jan 26, 2021 at 21:07 history edited John Machacek CC BY-SA 4.0
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Jan 26, 2021 at 19:12 comment added John Machacek Yes my apologizes. I was too hasty in my office before teaching :). I can leave it up if helpful otherwise delete. It seems @GjergjiZaimi has already found a better reference.
Jan 26, 2021 at 17:29 comment added Gjergji Zaimi The relevant paper is the one by Erdos and Posa referenced there. It shows that the best lower bound for the OP is of the form $O(d/\log d)$.
Jan 26, 2021 at 17:18 comment added H A Helfgott Well, I am asking whether one can bound the number of edge-disjoint cycles from below by $d/1000$ (say), so the statement given doesn't quite answer my question. I will follow the reference.
Jan 26, 2021 at 17:16 history answered John Machacek CC BY-SA 4.0