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An infinite family of graphs ${\cal F}$ is called feasible if for any pair ofintegers $(n,m)$, $n \geq 1$, $0 \leq m \leq \binom{n}{2}$, there is a member$G \in {\cal F}$ such that $G$ has $n$ vertices and $m$ edges. We prove thatgiven a graph $G$, the family ${\cal F}$$(G)$ of all induced $G$-free graphs isfeasible if and only if $G$ is not $K_k$, $K_k\backslash K_2$,$\overline{K_k}$, $\overline{K_k\backslash K_2}$, for $k \geq 2$.

The Feasibility Problem -- the family ${\cal F}$$(G)$ of all induced $G$-free graphs