Show HN: Creating groups of people so everyone always meets someone new

A writeup of my thought process: https://github.com/roshkins/Partnerings

I discovered this on my own, I would love to learn about any related math. I can see Combinatorics, possibly Group Theory, and maybe coloring a graph as relevant related topics.

I also learned that this is similar the problem of Gay Dating, although no one generalized it to multiple people.

Would love some thoughts!