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Everything about Matching polytope
Shape representing matchings in a graph
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. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Matching polytopeA 5-minute orientation
- Skim a recent paper: On (Random-Order) Online Contention Resolution Schemes for the Matching Polytope of (Bipartite) GraphsInfluential work since 2022
- Pick up a classic book: Linguistic structure predictionThe most-reprinted book on the subject
- Read the landmark paper: The Matching Polytope has Exponential Extension ComplexityCited 71 times
- Go sideways: Kőnig's theorem (graph theory)A closely related topic
- Go sideways: Fractional matchingA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
The Matching Polytope has Exponential Extension Complexity
On a Representation of the Matching Polytope Via Semidefinite Liftings
Establishing the matching polytope
On the stable b-matching polytope
On the fractional matching polytope of a hypergraph
The perfect matching polytope and solid bricks
When Is the Matching Polytope Box-Totally Dual Integral?
Maximal matching polytope in trees
🆕 Influential since 2022
📚 Books worth reading
Linguistic structure predictionNoah A. Smith · 2011
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Kőnig's theorem (graph theory) In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig (1931), describes an equivalence between the maximum matching problem…
- Fractional matching In graph theory, a fractional matching is a generalization of a matching in which, intuitively, each vertex may be broken into fractions that are matched…
- Unimodular matrix In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible…
- Rainbow matching In the mathematical discipline of graph theory, a rainbow matching in an edge-colored graph is a matching in which all the edges have distinct colors.…
- Polyhedral combinatorics Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the…
- Integral polytope In geometry and polyhedral combinatorics, an integral polytope is a convex polytope whose vertices all have integer Cartesian coordinates. That is, it…
- Perfect matching In graph theory, a perfect matching in a graph is a matching that covers every vertex of the graph. More formally, given a graph G with edges E and vertices…
- Matching preclusion In graph theory, a branch of mathematics, the matching preclusion number of a graph G {\displaystyle G} , denoted m p ( G ) {\displaystyle \mathrm {mp}…