In the previous subsection, we have described the efficient computation of all maximal cliques having a specific triangle t as their lowest element. To provide truly output-sensitive algorithms we have to notice that some of those cliques, say M, might not be maximal overall, since there might be a triangle s(t') with hypotenuse t' such that M' = M ⋃ s(t') is also a clique. Clearly t' is lower than t. Note that M' will be found when computing the maximal cliques with lowest element t'.