The complement of a maximal independent set, that is, the set of vertices not belonging to the independent set, forms a minimal vertex cover. That is, the complement is a vertex cover, a set of vertices that includes at least one endpoint of each edge, and is minimal in the sense that none of its vertices can be removed while preserving the property that it is a cover. Minimal vertex covers have been studied in statistical mechanics in connection with the hard-sphere lattice gas model, a mathematical abstraction of fluid-solid state transitions.