Before tackling the proof let us rephrase the problem in graph-theoretic terms. We interpret the people as the set of vertices V and join two vertices by an edge if the corresponding people are friends. We tacitly assume that friendship is always two-ways, that is, if u is a friend of v, then v is also a friend of u, and further that nobody is his or her own friend.
CITATION STYLE
Aigner, M., & Ziegler, G. M. (2018). Of friends and politicians. In Proofs from THE BOOK (pp. 307–309). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-662-57265-8_44
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