Let White have the two bishops. Given any setup, has the maximum number of moves to forced mate been calculated? If not, are there any bounds on this number?
Of course, information on extensions of this problem to say any rectangular board, are also welcome.
I should note that for a 2xn board checkmate isn't possible. Also, for m >= 3, with n >= m without loss of generality, I'm not certain whether forced mate is always possible. I would say though that it is given m,n sufficiently large though.
To update let the bishops be on opposite colored squares, of course.