Assume that every pair of people are (mutual) friends or enemies.
Show that in a group of 10 people, there are either 3 mutual friends or 4
Hint: Fix one person X. Start out by observing that X has either k friends
or 10-k enemies for an appropriately chosen k.
The Attempt at a Solution
A proof was shown in class for the case where there are 6 people, that involved a K6 graph. Is there any way to do this problem without using a graph since a K10 graph is quite large?