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