We define the triangle factoring problem as in Triangle Factors in Random Graphs, which is, given a simple undirected graph of 3n nodes, find a subset of edges dividing vertices into n vertex-disjoint triangles.

I’ve seen some papers discussing about the probability of such a factoring exists, but I’m unaware of any non-trivial algorithm solving this problem or any reductions. Is it NP-Complete? or, is it in P?