Given a complete graph, what is the maximum number of triangles that have no edges the same?
For example, two triangles that have a coinciding edge don't work (note that intersecting is fine).
For example, if we have a complete graph with 6 vertices labeled 1-6 clockwise, the two triangles determined by vertices 1, 3, 4 and vertices 1, 5, 6 are okay but the two triangles determined by vertices 2, 3, 4 and vertices 3, 4, 5 are not because the 4-5 edge coincides. Any help would be appreciated!