MathDB

Let

n, k

be positive integers with

k \geq 3

. The edges of of a complete graph

K_n

are colored in

k

colors, such that for any color

i

and any two vertices, there exists a path between them, consisting only of edges in color

i

. Prove that there exist three vertices

A, B, C

K_n

, such that

AB, BC

and

CA

are all distinctly colored.

Problem Statement