Extremal copositive matrices with minimal zero supports of cardinality two

Abstract

Let A ∈ C n be an extremal copositive matrix with unit diagonal. Then the minimal zeros of A all have supports of cardinality two if and only if the elements of A are all from the set {−1, 0, 1}. Thus the extremal copositive matrices with minimal zero supports of cardinality two are exactly those matrices which can be obtained by diagonal scaling from the extremal {−1, 0, 1} unit diagonal matrices characterized by Hoffman and Pereira in 1973.