In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors. Using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs, including those used in quantum information and suspensions of cubic planar graphs.
In this thesis we investigate a number of problems related to 2-level polytopes, in particular from ...
The max-cut problem is a fundamental and much-studied NP-hard combinatorial optimisation problem, wi...
A graph G is said to be a set graph if it admits an acyclic orientation that is also extensional, in...
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut poly...
In linear programming one can formulate many combinatorial optimization problems as optimizing a lin...
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exp...
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exp...
Courcelle’s theorem states that given an MSO formula ϕ and a graph G with n vertices and treewidth τ...
A linear extension of a polytope is any polytope which can be mapped onto via an affine transformati...
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of k...
We prove that the extension complexity of the independence polytope of every regular matroid on n el...
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of k...
Let P be a finite poset. By definition, the linear extension polytope of P has as vertices the chara...
The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that af...
We calculate the growth rate of the complexity function for polytopal cut and project sets. This gen...
In this thesis we investigate a number of problems related to 2-level polytopes, in particular from ...
The max-cut problem is a fundamental and much-studied NP-hard combinatorial optimisation problem, wi...
A graph G is said to be a set graph if it admits an acyclic orientation that is also extensional, in...
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut poly...
In linear programming one can formulate many combinatorial optimization problems as optimizing a lin...
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exp...
We exhibit an n-node graph whose independent set polytope requires extended formulations of size exp...
Courcelle’s theorem states that given an MSO formula ϕ and a graph G with n vertices and treewidth τ...
A linear extension of a polytope is any polytope which can be mapped onto via an affine transformati...
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of k...
We prove that the extension complexity of the independence polytope of every regular matroid on n el...
We study the linear extension complexity of stable set polytopes of perfect graphs. We make use of k...
Let P be a finite poset. By definition, the linear extension polytope of P has as vertices the chara...
The extension complexity xc(P) of a polytope P is the minimum number of facets of a polytope that af...
We calculate the growth rate of the complexity function for polytopal cut and project sets. This gen...
In this thesis we investigate a number of problems related to 2-level polytopes, in particular from ...
The max-cut problem is a fundamental and much-studied NP-hard combinatorial optimisation problem, wi...
A graph G is said to be a set graph if it admits an acyclic orientation that is also extensional, in...
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