On the classes of fully copositive and fully semimonotone matrices

In this paper we consider the class C-0(f) of fully copositive and the clas s E-0(f) of fully semi-monotone monotone matrices. We show that C-0(f) matr ices with positive diagonal entries are column sufficient. We settle a conj ecture made by Murthy and Parthasarathy to the effect that a C-0(f) boolean AND Q(0) matrix is positive semidefinite by providing a counterexample. We finally consider E-0(f) matrices introduced by Cottle and Stone (Math. Pro gram. 27 (1983) 191-213) and partially address Stone's conjecture to the ef fect that E-0(f) boolean AND Q(0) subset of or equal to P-0 by showing that E-0(f) boolean AND D-c matrices are P-0, where D-C is the Doverspike class of matrices. (C) 2001 Elsevier Science Inc. All rights reserved.