On graphs with a large number of edge-colorings avoiding a rainbow triangle

Inspired by previous work of Balogh (2006), we show that, given r≥5 and n large, the balanced complete bipartite graph Kn∕2,n∕2 is the n-vertex graph that admits the largest number of r-edge-colorings for which there is no triangle whose edges are assigned three distinct colors. Moreover, we extend this result to lower values of n when r≥10, and we provide approximate results for r∈{3,4}.