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Dividing a gathering for friends


Let’s say there is a gathering where among any three people there are two friends. Is it true that people at such gathering can always be divided into two groups in a way that every two people in one group are friends?

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1 answer to this question

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This appears to be an example of the monochromatic triangle problem and its connection to Ramsey's theorem

Specifically, in any group of at least six persons, there will be a subgroup of at least three persons in which there are either no friendships (a scenario excluded by the question) or each person in the subgroup is friends with each other person in the subgroup (the scenario that the question wants to prove is implied by the exclusion of the former). To answer the question, yes it is true.


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