There's some Interesting graph theory problem somewhere in here about finding out if a network of N people in M relationships must include at least one gay person.
A relationship graph which requires no gay relationships is called a bigraph (honest, I'm not making this up) or bipartite.
That follows because if you can two color the graph so that edges only connect different colors, you just assign male to one color and female to the other.
This means there's a tone of mathematical identities describing this. Wikipedia has a good introduction.
Very neat. But the fun part of this is that if you're poly/into more than one person, you are now a part of the LGBT group, not the straight one.
Note the above image, where the triangle shape requires that every person be into another person, with the tension being that if it's cishet, they have to choose only one person.
We aren't checking to see if a shape with LGBT people works, we know those do. We are checking to see if a cishet triangle is even possible.
Yes. My girlfriend’s husband is cishet, it has nothing to do with his willingness to have multiple partners, just the fact that he’s an amab man who exclusively is attracted to women. His wife happens to be pansexual and dating a lesbian, but that has no impact on his orientation
Even numbers are pretty easy to solve at least. They can be straight or lgbt.
I posit that any love shape that includes an odd number of participants requires some form of deception, or at least one LGBT person in order to be valid.