Sparse graphs

For positive integers k and l a graph G=(V,E) is called $$(k,l)$$ -sparse if $$i_G(X)\leq k|X|-l$$ holds for every $$X\subseteq V$$ , $$|X|\geq l/k$$ . If $$|E|=k|V|-l$$ we say that G is a $$(k,l)$$ -graph. For characterizations of $$(k,l)$$ -sparse graphs, see the paper of Fekete and Szegő and Lee and Streinu .