There is a graph $G=(V,E)$, where $|V|=n$. Let's consider every induced subgraph of $G$ with $k$ vertices. I denote cardinality of $l$-th induced subgraph (its edges) as $a_{l}$ and i call it a $l$-th value of a graph.
There is given a system of values $(a_{1},...,a_{{n\choose k}})$. Find the a way to decide whether this system is set of values of some graph.
I even don't know how to approach this problem.
Regards.