this post was submitted on 16 Sep 2024
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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.
https://en.m.wikipedia.org/wiki/Bipartite_graph
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.
A relationship isn't LGBT; a person is. A cishet man who has two bi/pan female partners who date each other isn't LGBT because his partners are queer.