ambassador problem

[yzb25]

there are 2 * [X] ambassadors. Each ambassador has [X] - 1 adversaries. Adversarial relationships are mutual, and ambassadors who are adversaries refuse to sit next to eachother.

Thankfully, irrespective of who is who's adversary, you can always seat them around a round table in such a manner so that no ambassador sits next to one of their adversaries.

why? how do you ensure this happens?

(i.e. prove that there always exists a valid seating)

UPDATE: I was expecting like one reply maybe I'm basically crying tears of joy rn.

I apologize if the question was written opaquely. You must explain how a valid seating exists, irrespective of who is who's adversary - meaning every friend/enemy structure must be accounted for. Otherwise, Voss' solution also finds a valid seating for at least one friend/enemy structure for each X. Aamirus' proof elegantly lays out a way of breaking down a considerably larger number of cases though. From my own computations, it seems many are decomposable in the manner she described, but I honestly haven't considered X>4.

Mattzed gives a correct outline of a proof and thus a correct answer. tbh, I was thinking about this one for a long ass time and never figured it out. So congrats! Of course, he's put it in spoilers, so I encourage anyone else interested to not view the solution and try it for yourself.