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

Zeev Nutov, Michal Penn

Research output: Contribution to journalArticlepeer-review

Abstract

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 = PnLO for n ≤ 5, while for n > 5 PnLO ⊂ PnC. Borobia gave a complete characterization of the extreme points of PnC with values in {0, I, 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.

Original languageEnglish
Pages (from-to)149-159
Number of pages11
JournalLinear Algebra and Its Applications
Volume233
DOIs
StatePublished - 15 Jan 1996
Externally publishedYes

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