# Time complexity of the triangle factoring problem

We define the triangle factoring problem as in Triangle Factors in Random Graphs, which is, given a simple undirected graph of $$3n$$ nodes, find if there's 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?

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