Abstract
It is not known who first raised the following problem or who gave it its human touch. Here it is:
Suppose in a group of people we have the situation that any pair of persons have precisely one common friend. Then there is always a person (the “politician”) who is everybody’s friend.
In the mathematical jargon this is called the friendship theorem.
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References
P. Erdős, A. Rényi & V. Sós: On a problem of graph theory, Studia Sci. Math. 1 (1966), 215-235.
A. Kotzig: Regularly k -path connected graphs, Congressus Numerantium 40 (1983), 137-141.
A. Kostochka: The nonexistence of certain generalized friendship graphs, in: “Combinatorics” (Eger, 1987), Colloq. Math. Soc. János Bolyai 52, North-Holland, Amsterdam 1988, 341-356.
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Aigner, M., Ziegler, G.M. (2010). Of friends and politicians. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00856-6_39
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DOI: https://doi.org/10.1007/978-3-642-00856-6_39
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