This question is influenced by the book Parameterized Algorithms by Marek Cygan, Fedor V. Fomin, Lukasz Kowalik, Daniel Lokshtanov, Dániel Marx, Marcin Pilipczuk, Michal Pilipczuk and Saket Saurabh.
You are the bodyguard of a bar in a small town, and every friday night the bar is very busy. Since the town is small, you know almost everyone, and all the conflicts among people.
The conflicts are mutual. If one wants to fight another, then you cannot assume the other will stop.
Your aim is to let in as many people as you can. But the problem is, if you let a pair conflicting people in, then they will probably fight, causing a trouble.
Alice and Bob are dating. Therefore, if one fights to someone, the other will also fight.
Charlie and Daniel are nemeses. Thus, if one dislikes another person, the other will not fight with that person, and vice versa.
Charlie is a womanizer who does not like single men to be around him while he's drinking in a friday night.
Erik has no problems except Charlie. He plain doesn't like Charlie.
Fred and Jennifer are a couple, and hate Bob because Bob cheated on his former girlfriend.
Hillary is Bob's ex-girlfriend, and does not like Alice at all, because Bob left her for Alice.
Gerald is very angry at Hillary because she is getting involved into another couple's relationship.
Larry is a very good friend of Bob, but he doesn't like Alice since Alice does not let Bob to go out with Larry.
Question: Who should you let in, and who should you prevent from entering the bar in order to prevent a potential fight? Remember that you want to let in as many people as you can.