Karp hardness of directed monochromatic triangle problem
All directed graphs can be edge-partitioned into two subgraphs that are acyclic and therefore triangle free.

Let $\prec$ be any total ordering of the vertices. For each edge $(u, v) \in A$, put it in $A_1$ if $u \prec v$, and in $A_2$ otherwise. Both $(V, A_1)$ and $(V, A_2)$ must be acyclic.