TY - JOUR
T1 - On non-{0, 1, 1/2} extreme points of the generalized transitive tournament polytope
AU - Nutov, Zeev
AU - Penn, Michal
PY - 1996/1/15
Y1 - 1996/1/15
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=21844515617&partnerID=8YFLogxK
U2 - 10.1016/0024-3795(94)00063-8
DO - 10.1016/0024-3795(94)00063-8
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:21844515617
SN - 0024-3795
VL - 233
SP - 149
EP - 159
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -