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A simple graph-product type construction shows that for all natural numbers$r \ge q$, there exists an edge-coloring of the complete graph on $2^r$vertices using $r$ colors where the graph consisting of the union of arbitrary$q$ color classes has chromatic number $2^q$. We show that for each fixednatural number $q$, if there exists an edge-coloring of the complete graph on$n$ vertices using $r$ colors where the graph consisting of the union ofarbitrary $q$ color classes has chromatic number at most $2^q -1 $, then $n$must be sub-exponential in $r$. This answers a question of Conlon, Fox, Lee,and Sudakov.

A sub-exponential transition of the chromatic generalized Ramsey numbers