In graph theory, the matching polytope of a given graph is a geometric object representing the possible matchings in the graph. It is a convex polytope each of whose corners corresponds to a matching. It has great theoretical importance in the theory of matching.[1]: 273–285
^Lovász, László; Plummer, M. D. (1986), Matching Theory, Annals of Discrete Mathematics, vol. 29, North-Holland, ISBN 0-444-87916-1, MR 0859549
theory, the matchingpolytope of a given graph is a geometric object representing the possible matchings in the graph. It is a convex polytope each of whose...
the stable matchingpolytope or stable marriage polytope is a convex polytope derived from the solutions to an instance of the stable matching problem....
perfect matchingpolytope of a graph is a polytope in R|E| in which each corner is an incidence vector of a perfect matching. Envy-free matching Maximum-cardinality...
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the n {\displaystyle n} -dimensional...
The Birkhoff polytope Bn (also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matchingpolytope of the complete...
programming polyhedral description of the matchingpolytope, yielding an algorithm for min-weight matching. As elaborated by Alexander Schrijver, further...
combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it is a polytope that equals the convex...
the fractional matchingpolytope of G is a convex polytope that represents all possible fractional matchings of G. It is a polytope in R|E| - the |E|-dimensional...
vertex coordinates are 0 or 1 are exactly the order polytopes. Stable matchingpolytope, a convex polytope that defines a distributive lattice on its points...
labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope. The Oxford English...
the extension complexity of the polytopes arising in this way. For instance, it is known that the matchingpolytope has exponential extension complexity...
graphs Thomas Rothvoss for his work on the extension complexity of the matchingpolytope. 2021: Béla Csaba, Daniela Kühn, Allan Lo, Deryk Osthus, and Andrew...
dual integrality. Other specific well-known integral LPs include the matchingpolytope, lattice polyhedra, submodular flow polyhedra, and the intersection...
apply linear programming to the order polytope of the partial order of rotations, or to the stable matchingpolytope. An alternative, combinatorial algorithm...
polynomial time. This is a straightforward consequence of Edmonds' matchingpolytope theorem. Applications of fractional graph coloring include activity...
face, an edge of the face, a vertex of the edge, and the null polytope. An abstract polytope is said to be regular if its combinatorial symmetries are transitive...
spaces that contain the two polytopes (not necessarily of the same dimension) which induces a bijection between the polytopes. Manuel Blum and Sampath Kannan (1995)...
Kleetope of a polyhedron or higher-dimensional convex polytope P is another polyhedron or polytope PK formed by replacing each facet of P with a shallow...
are only three convex regular polytopes: the simplex as {3,3,...,3}, the hypercube as {4,3,...,3}, and the cross-polytope as {3,3,...,4}. In three dimensions...
graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius of Perga, who studied a related circle-packing...
Krein–Milman theorem) every convex polytope is the convex hull of its vertices. It is the unique convex polytope whose vertices belong to S {\displaystyle...
Global Information