Counting edge-colorings of a complete graph avoiding a rainbow $K_4$

Fabricio S. Benevides, Josefran de O. Bastos

For $k,r,n$ natural numbers let ${\rho }_{r,k}(K_n)$ 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 e…