There is given a complete graph $B=K_{n}$.
I make a special set of marked edges. Lets call it $A$. Its construction is following:
Let $k=0$ and $A$ is empty and it has the same vertices as $B$.
First step. I add to $A$ any edge from $B$.
Next steps. If there exists new edge $e$ which is adjacent to $k$ edges from $A$, then i add $e$ to $A$. Otherwise i add a one to $k$.
Finally. Algorithm stops when every $l$-clique from $B$ has at least one edge from $A$.
How many edges $A$ contain?
I know the topic is connected with finding independent set of edges, but i can't find a application of it here.
Maybe some of you see the solution?
Regards.