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MathNet 2020 — Math Olympiad Vault — Part 01 Question 75

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 75

Each vertex of complete bipartite graph $K_{128,128}$ is occupied by a person. In the beginning all the persons are unfamiliar. If the persons are in the adjacent vertices, they immediately get to know each other. It is allowed to take several edges without common vertices and swap the persons in the endpoints of each edge. What is the minimum number of such operations we need to get all the persons acquainted?