My understanding is that there are at least two types of Swiss tournament:

- Fixed length: the tournament lasts a fixed number of rounds, which may be set as a function of the initial number of players or just chosen some other way. If this number is set too low relative to the number of players, it is possible for the tournament to end with more than one player having won all of their games.
- Variable length: the tournament ends when there is only one player left that has won all of their games. With a pairing method that always assigns players with all wins with each other (except for maybe one odd one left out), this would most likely take no more than ceil(log2(N)) rounds.

Knowing the constant here is crucial. Hopefully, it is only a fraction of N, rather than a multiple.

Does this mean that Swiss tournaments are actually fixed length, but with the number of rounds being a function of the initial number of players?

I suppose that yet another possibility is that after each round, the number of played rounds is compared to a function of the number of remaining participants (those that have not chosen to drop out), and ending the tournament if the former is greater than the latter.