On graphs with a large number of edge-colorings avoiding a rainbow triangle. (December 2017) - Hoppen, Carlos; Lefmann, Hanno; Odermann, Knut
Abstract: Inspired by previous work of Balogh (2006), we show that, given r ≥ 5 and n large, the balanced complete bipartite graph K n ∕ 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 .