Color coding to get an FPT algoirthm for k disjoint triangles
The dynamic programming algorithm goes over all subsets of $[3k]$ whose size is a multiple of 3, in nondecreasing order of size. For each such non-empty subset, it goes over all $O(n^3)$ triplets of vertices, and for each one, it performs a single table look-up. Therefore the running time is $O^*(2^{3k} n^3)$, where $O^*$ hides $\operatorname{poly}(k)$ factors which are needed to manipulate indices.