## Abstract

The acyclic tournaments of order n form the linear ordering polytope P^{n}_{LO}. The generalized transitive tournaments of order n form the polytope P^{n}_{C}, which contains the linear ordering polytope. It is known that the integral extreme points of P^{n}_{C} coincide with those of P^{n}_{LO}. Dridi showed that P^{n}_{LO} = P^{n}_{LO} for n ≤ 5, while for n > 5 P^{n}_{LO} ⊂ P^{n}_{C}. Borobia gave a complete characterization of the extreme points of P^{n}_{C} with values in {0, I, 1/2}. It was mentioned by Brualdi and Hwang that no extreme points of P^{n}_{C} 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 P^{n}_{C} with values not in {0, 1, 1/2}. We also prove that these non-half-integral extreme points of P^{n}_{C} violate certain diagonal inequalities which are facet defining for P^{n}_{LO}.

Original language | English |
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Pages (from-to) | 149-159 |

Number of pages | 11 |

Journal | Linear Algebra and Its Applications |

Volume | 233 |

DOIs | |

State | Published - 15 Jan 1996 |

Externally published | Yes |