Alon, Balogh, Keevash, and Sudakov proved that the (k-1)-partite Turán graph maximizes
the number of distinct r-edge-colorings with no monochromatic K_k for all fixed k and r=2,3,
among all n-vertex graphs. In this paper, we determine this function asymptotically for r=2
among n-vertex graphs with a sublinear independence number. Somewhat surprisingly,
unlike Alon, Balog, Keevash, and Sudakov's result, the extremal construction from Ramsey--
Turán theory, as a natural candidate, does not maximize the number of distinct edge …

Alon, Balogh, Keevash and Sudakov proved that the $(k-1) $-partite Tur\'an graph
maximizes the number of distinct $ r $-edge-colorings with no monochromatic $ K_k $ for all
fixed $ k $ and $ r= 2, 3$, among all $ n $-vertex graphs. In this paper, we determine this
function asymptotically for $ r= 2$ among $ n $-vertex graphs with sub-linear independence
number. Somewhat surprisingly, unlike Alon-Balogh-Keevash-Sudakov's result, the extremal
construction from Ramsey-Tur\'an theory, as a natural candidate, does not maximize the …