Is max number of rounds variable for Swiss tournaments?

A Swiss tournament (like a round robin) can have n - 1 rounds for an even number of participants, and n rounds for an odd number having 1 bye per round. It seems it's not always possible to reach those round maximums while offering participants a shot at the same number of points per round. Consider this... show more A Swiss tournament (like a round robin) can have n - 1 rounds for an even number of participants, and n rounds for an odd number having 1 bye per round.

It seems it's not always possible to reach those round maximums while offering participants a shot at the same number of points per round.

Consider this 6 player example, 1point per win, half a point per tie, FIDE pairings:

= 1st round =
1v4 - 4 wins
2v5 - tie
3v6 - 6 wins

standings: 4 (1.0), 6 (1.0), 2 (0.5), 5 (0.5), 1 (0.0), 3 (0.0)

= 2nd round =
4v6 - 6 wins
2v1 - 2 wins
5v3 - tie

standings: 6 (2.0), 2 (1.5), 4 (1.0), 5 (1.0), 3 (0.5), 1 (0.0)

= 3rd round =
6v2 - 6 wins
3v1 - 3 wins
4v5 - 4 wins

standings: 6 (3.0), 2 (1.5), 3 (1.5), 5 (1.0), 4 (1.0), 1 (0.0)

= 4th round (where the wall is hit) =

1 has not played 5 & 6
2 has not played 3 & 4
3 has not played 2 & 4
4 has not played 2 & 3
5 has not played 1 & 6
6 has not played 1 & 5

If 1 is paired with 5, 6 can't be paired. If 1 is paired with 6, 5 can't be paired.

Given this, does the tournament come to an end? I suppose a round could be added, but then there would be a variable number of matches per round. Any guidance here is greatly appreciated!
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