In a complete graph on(n + 1)!vertices each of the edges are colored with one of n colors (n 2).Use the Ramsey number, Ramsey theory,or Pigeonhole principleto prove that it is always possible to find such vertices A, B, C, that edges AB, AC, BC are of the same color.Note that there are(n+1)! vertices, Not n+1. Induction proof may also be used in this problem.

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