P-c-matrices and the linear complementarity problem

We introduce a new matrix class P-c, which consists of those matrices M for which the solution set of the corresponding linear complementarity problem is connected for every q is an element of R(n). We consider Lemke's pivotal method from the perspective of piecewise linear homotopies and normal maps and show that Lemke's method processes all matrices in P-c boolean AND Q(0). We further investigate the relationship of the class P-c to other known matrix classes and show that column sufficient matrices are a subclass of P-c, as are 2 x 2 P-0-matrices.