On non-{0, 1/2, 1} extreme points of the generalized transitive tournament polytope Original Research Article

The acyclic tournaments of order n form the linear ordering polytope PnLO. The generalized transitive tournaments of order n form the polytope PnC, which contains the linear ordering polytope. It is known that the integral extreme points of PnC coincide with those of PnLO. Dridi showed that PnLO = PnC for n less-than-or-equals, slant 5, while for n > 5PnLO subset of PnC. Borobia gave a complete characterization of the extreme points of PnC with values in {0, 1, 1/2}. It was mentioned by Brualdi and Hwang that no extreme points of PnC with values not in {0, 1, 1/2} are known. In this paper we present a method for obtaining a family of extreme points of PnC with values not in {0, 1, 1/2}. We also prove that these non-half-integral extreme points of PnC violate certain diagonal inequalities which are facet defining for PnLO.