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A balanced edge-coloring of the complete graph is an edge-coloring such thatevery vertex is incident to each color the same number of times. In this shortnote, we present a construction of a balanced edge-coloring with six colors ofthe complete graph on $n=13^k$ vertices, for every positive integer $k$, withno rainbow $K_4$. This solves a problem by Erd\H{o}s and Tuza.

A note on balanced edge-colorings avoiding rainbow cliques of size four