Given the problem 1/m-Clique (half clique third clique and so on) ,**I wanted to know if the following reduction is correct**, since every solution I've seen in the internet was far more complicated and most of the times used the reduction from 1/(m-1) Clique problem, instead of doing it directly from the Clique problem. So I want to show a pol' reduction from Clique to 1/m-Clique for some m. Given (G,k) ,build G': take G and add (n-k) vertices and connect them to every node in G (so if there's an k clique, now there will be an n clique), and add m*n-(2n-k) isolated vertices, return (G',n). overall if there's a k clique in G, there will be an n clique in G', and m*n vertices, hence n/m*n=1/m clique. If G doesn't have a k clique (nor j>k clique) no n-clique will be constructed in G' (we only add n-k nodes which can "help" in forming a clique), hence no 1/m clique.

1/m Clique reduction