I'm looking for a solution to the following problem.
Given $n = a\cdot (b-1) + 1$ players, $a$ and $b$ being integers with $a \leq b$, I want to schedule a round-robin tournament where every player plays every other player exactly once in a series of days, such that every day at most $b$ players play, and they play all the matches between themselves on that day. Furthermore, a given player cannot play in more than $a$ of the days.
The scheduling might not be possible for all values of $a$ and $b$ but it is possible at least for the special case where $a=b$ and a solution only for that case would also be good.