Notes on the Deficiency-One Theorem: Multiple linkage classes

The Deficiency-One Theorem tells us about certain chemical reaction systems that they cannot admit multiple interior equilibria. The theorem was proven by Feinberg. In this paper we provide a relatively short proof of that theorem. We also extend that result by giving an equivalent condition to the fact that the set of interior equilibria is nonempty for a chemical reaction system considered in the Deficiency-One Theorem.