Proper edge colorings of complete graphs without repeated triangles - Botler, Fábio; Colucci, Lucas; Matias, Paulo; Mota, Guilherme; Parente, Roberto; Secco, Matheus (Anais do Encontro de Teoria da Computação (ETC); 2022: Anais do VII Encontro de Teoria da ComputaçãoDO - 10.5753/etc.2022.222917, 2022)
In this paper, we consider the problem of computing the minimum number of colors needed to properly color the edges of a complete graph on $n$ vertices so that there are no pair of vertex-disjoint triangles colored with the same colors. This problem was introduced recently (in a more general context) by Conlon and Tyomkyn, and the corresponding value was known for odd $n$. We compute this number for another infinite set of values of $n$, and discuss some small cases.