# Graph theory dinner party problem

In a party of 6 people is it true that there exists four people either all do or all do not knowing each Other?

I know it's false, and have the solution but not quite sure where to begin with the justification for these types of problem, any tips will be much appreciated, thanks!

-
Give a counterexample. Call your people $1$ to $6$, and specify who knows whom and who doesn't. You might do it in words, or with a graph, joining pairs who know each other with a blue line, and people who don't with a red line.
The simplest counterexample is $1$, $2$, $3$ know each other, but nobody else. And $4$, $5$, $6$ know each other, but nobody else. It is obvious that there is no group of $4$ mutual acquaintances, and no group of $4$ mutual strangers.