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Counting edge-colorings of a complete graph avoiding a rainbow $K_4$
For $k, r, n$ natural numbers let $ρ_{r,k}(K_n)$ be the number of $r$-edge-colorings of $K_n$ that do not contain a rainbow copy of a $K_k$, that is, a copy of $K_k$ in which all edges receive different colors. When $k=3$, the quantity $ρ_{r,3}(K_n)$ represents the number of Gallai Colorings. It was
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