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Source: Bundeswettbewerb Mathematik 2024, Round 2 - Problem 4
September 13, 2024
combinatoricscombinatorics proposedgraph theory
Problem Statement
In Sikinia, there are cities. Between some of them there are flight connections, which can be used in either direction. No city has a direct flight to all other cities. It is known, however, that there is a positive integer with the following property: For any cities in Sikinia, there is another city which is directly connected to all these cities.
Determine the largest possible value of .