An upper bound for the number of maximal independent sets in a graph

Let $T(G)$ be the number of maximal independent sets, $M(G)$ be the number of generated matchings in a graph $G$. We prove the inequality $T(G)\le M(G)+1$. As a corollary, we derive the bound $T(G)\le((m-m_1)/p+1)^p+m_1$ for a graph containing no generated subgraph $(p+1)K_2$, where $m$ is the number of edges and $m_1$ is the number of dominating edges. This inequality differs from the Balas–Yu conjecture only in the presence of the last term.