Problem #PRU-5289

Problems Discrete Mathematics Mathematical logic

Problem

In a parliament with only one house every member had not more than three enemies. Is it possible split this parliament into two separate houses in such a way that each member will have not more than one enemy in the same house as them. We assume that hard feelings among members of parliament are mutual, namely if \(A\) recognises \(B\) as their enemy, then \(B\) also recognises \(A\) as their enemy.