This is a famous result. See:
Theorem on friends and strangers - Wikipedia, the free encyclopedia
How does one show that in a kindergarten group of 6 children that there are 3 who mutually like each other or there are 3 who mutually hate each other?
Note: Assume that every two kids either like or hate each other and that there are no neutral relationships.
This is a famous result. See:
Theorem on friends and strangers - Wikipedia, the free encyclopedia