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.
“Get out to vote” is a direct instruction. It means you personally should go and vote.
“Get out the vote” means you should get everyone else out to vote. “Vote” is being used as a mass noun that you want to make as large as possible -by getting it out and making sure people turn up.