Maximum of K3 disjoint subgraphs of graph

Question

I am trying to solve a following problem: We have some graph. How to find (only number) maximum of K3 complete graphs which are subgraphs of input graph and are disjoint to each other.

I DO NOT need a code, a complete solution. I need an advice where to start. I thought about DFU and some traversing but it doesn't give a solution, at least not with some good time complexity.

Answer 1

By disjoint I presume you mean any two triangles do not even share a vertex.

This is going to be NP-Hard.

Partition into triangles is NP-Complete, and can be reduced to your problem.

By constructing a graph of the triangles: each triangle is a vertex and two triangles are adjacent if they share a node. You could reduce it to the largest independent set problem, which probably has a lot of literature on algorithms/approximation algorithms etc.