Random nagging thought of the day - math nerdiness

So I just ate lunch and in one way or another a math problem came into my head and I can't solve the problem off the top of my head (although I think I should be able to - quite indicative of my mathematical deficiencies by now)

Somehow, my train of thought wandered into speed dating. (Oh cuz I think I just watched the 40-year-old Virgin recently). Let's say there are m males, f females in one speed dating session. Now to minimize the number of rounds you'd have to go through, it's clear that you just take the higher of the two numbers. (Just think of it in terms of a ring with the lower number of sexes stationary and the higher number going around in the ring...? ok whatever, not really relevent)

But then my perverted mind started envisioning a speed dating...with homosexuals. What would the optimal number of rounds be so that for n number of homosexuals every homosexual has a chance to meet every other homosexual but only once? (even with the occasional odd man/woman out, etc) And if so, how would the schedule for one homosexual look like in this session and how do we ensure that there are no conflicts of schedule(or interest lol)? Now if your mind was very quick on these combinatorics stuff you might already be wondering how this is different than the problem with the number of handshakes with n people. Well, it is, but the additional twist is that within one round, you can have as many pairings as possible (but you might get leftover pairs that've already met? I dont' know) You can also apply that restriction to handshake sessions but hey, I thought of homosexual speed dating first so too bad. It's more plausible anyways. :P

So yeah, I know the number of pairings in total would be n(n-1)/2 (or whatever the triangle number is, lol). But I'm not sure how the number of rounds would collapse depending on n. Also, what if you had m gays and f lesbians? How would the minimum number of rounds be defined as a function of (m, f) then? (with no pairings between gays and lesbians, of course)

If one of you math nerds could help me out, I'd really appreciate it :) Yes, I know. This is one of the most absurd math problems I've conjured up yet. But hey, that's what you get from terrible caf food with insufficient nutrients. :)