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May 2, 2022 at 14:54 comment added Stanley Yao Xiao I believe this gives me a good idea for what happens in the regime where $n$ is large compared to $k$. I am also interested in the reverse regime, when $n$ is small compared to $k$; see this question: mathoverflow.net/questions/421589/…
May 2, 2022 at 13:10 comment added Brendan McKay @StanleyYaoXiao I'm only considering the event that the weight is k, which occurs for 2 of the $2^k$ possible values of $b(u)+b(v)$. The analysis is the same no matter which two values we are interested in.
May 2, 2022 at 12:55 comment added Stanley Yao Xiao It is not clear to me where you accounted for the fact that one needs to account for the maximum function to give the edge weights... could you please clarify?
May 2, 2022 at 10:51 history answered Brendan McKay CC BY-SA 4.0