I am aware that the traveling salesman problem (TSP) and the bottleneck TSP problem is NP-hard for complete directed graphs. I am also aware that regular TSP that allows a path with repeating is also NP-hard. However, I was not able to find a reference for the complexity of the bottleneck TSP problem with repeated nodes for complete graphs.
Also, I am curious if continuously removing the most costly edges until all nodes are not strongly connected actually solves this problem. I think that this method should solve this problem, but I was not sure about it.