scholarly journals Clique–Stable Set separation in perfect graphs with no balanced skew-partitions

2016 ◽  
Vol 339 (6) ◽  
pp. 1809-1825 ◽  
Author(s):  
Aurélie Lagoutte ◽  
Théophile Trunck
Keyword(s):  
Perfect Graphs ◽  
Stable Set ◽  
Set Separation

scholarly journals Decomposition techniques applied to the Clique-Stable set separation problem

2018 ◽  
Vol 341 (5) ◽  
pp. 1492-1501
Author(s):  
Nicolas Bousquet ◽  
Aurélie Lagoutte ◽  
Frédéric Maffray ◽  
Lucas Pastor
Keyword(s):  
Stable Set ◽  
Decomposition Techniques ◽  
Separation Problem ◽  
Set Separation

scholarly journals STRONG KOSZULNESS OF TORIC RINGS ASSOCIATED WITH STABLE SET POLYTOPES OF TRIVIALLY PERFECT GRAPHS

2014 ◽  
Vol 13 (04) ◽  
pp. 1350138 ◽  
Author(s):  
KAZUNORI MATSUDA
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Perfect Graphs ◽  
Stable Set ◽  
Necessary And Sufficient ◽  
Toric Rings

We give necessary and sufficient conditions for strong Koszulness of toric rings associated with stable set polytopes of graphs.

scholarly journals Stable Set Bonding in Perfect Graphs and Parity Graphs

1993 ◽  
Vol 59 (1) ◽  
pp. 1-14 ◽  
Author(s):  
D.G. Corneil ◽  
J. Fonlupt
Keyword(s):  
Perfect Graphs ◽  
Stable Set

scholarly journals Lift-and-project ranks of the stable set polytope of joined a-perfect graphs

2016 ◽  
Vol 210 ◽  
pp. 176-184
Author(s):  
S. Bianchi ◽  
M. Escalante ◽  
M.S. Montelar
Keyword(s):  
Perfect Graphs ◽  
Stable Set ◽  
Stable Set Polytope

scholarly journals Nearly Gorenstein Rings Arising from Finite Graphs

2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Takayuki Hibi ◽  
Dumitru I. Stamate
Keyword(s):  
Perfect Graphs ◽  
Stable Set ◽  
Gorenstein Rings ◽  
Finite Graphs ◽  
Multipartite Graphs ◽  
Complete Multipartite Graphs ◽  
Complete Multipartite

The classification of complete multipartite graphs whose edge rings are nearly Gorenstein as well as that of finite perfect graphs whose stable set rings are nearly Gorenstein is achieved.

scholarly journals Polyhedral approximations of the semidefinite cone and their application

2021 ◽  
Author(s):  
Yuzhu Wang ◽  
Akihiro Tanaka ◽  
Akiko Yoshise
Keyword(s):  
Initial Approximation ◽  
Semidefinite Relaxation ◽  
Stable Set ◽  
Cutting Plane Methods ◽  
Diagonally Dominant Matrices ◽  
Maximum Stable Set ◽  
Simple Expansion ◽  
Diagonally Dominant ◽  
Polyhedral Approximations ◽  
Semidefinite Cone

AbstractWe develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.

Sign in / Sign up

Export Citation Format

Share Document