Sets defining minimal vertex covers Original Research Article

Let V be a finite non-empty set of n elements, let r be a natural integer and let A = {A1, …, Ar} ⊂ P(V) be a non-empty set of subsets of V. In this paper the question arises whether there exists a graph G with vertex set V and whose minimal vertex cover sets are the elements of A. In order to solve this problem we characterize the set of minimal vertex covers of a graph by using special binary matrices.