A Polyhedral Description of Kernels

postprin

A Polyhedral Description of Kernels

MS30 Graph Theory - Part II of IIILet G be a digraph and let π(G) be the linear system consisting of nonnegativity, stability, and domination inequalities. We call G kernel ideal (resp. kernel Mengerian) if π(H) defines an integral polytope (resp. π(H) is totally dual integral) for each induced subgraph H of G. The purpose of this talk is to show that G is kernel ideal iff it is kernel Mengerian iff it contains none of three forbidden structures. (Joint work with Qin Chen and Xujin Chen

Recent Advances in Polyhedral Combinatorics

Combinatorial optimization searches for an optimal object in a finite collection; typically the collection has a concise representation while the number of objects is huge. Polyhedral and linear programming techniques have proved to be very powerful and successful in tackling various combinatorial optimization problems, and the end products of these methods are often integral polyhedra or min-max relations. This area of combinatorial optimization is called polyhedral combinatorics. In this talk I shall give a brief survey of our recent results on polyhedral combinatorics, including a tournament ranking with no errors, a polyhedral description of kernels, and a characterization of the box-totally dual integral (box-TDI) matching polytope

Recent Advances in Polyhedral Combinatorics

Organizers: Society of Graph Theory and Combinatorics, ORSC ; Center of Graph Theory, Combinatorics & Network of AMSS ; Yuncheng UniversityPlenary talkCombinatorial optimization searches for an optimal object in a nite collection; typically the collection has a concise representation while the number of objects is huge. Polyhedral and linear programming techniques have proved to be very powerful and successful in tackling various combinatorial optimization problems, and the end products of these methods are often integral polyhedra or min-max relations. This area of combinatorial optimization is called polyhedral combinatorics. In this talk I shall give a brief survey of our recent results on polyhedral combinatorics, including a tournament ranking with no errors, a polyhedral description of kernels, and a characterization of the box-totally dual integral (box-TDI) matching polytope