How to check whether graph of n vertex contains n/k disjoint k - complete graph by linear programming?

Question

Edges are given in form of Xij, which denotes whether there is edge in between i'th and j'th vertex. I am solving integer optimization problem and want to add this constraint to it.

Answer 1

Recently, I got a solution of it and wanted to share it.

I think this two conditions are sufficitent and necessary.

∀i Xi1 + Xi2...... XiN = K - 1

∀i, ∀j, ∀k Xij + Xjk + Xik != 2