The perfect matching polytope and solid bricks
نویسندگان
چکیده
منابع مشابه
The Perfect Matching Polytope and Solid Bricks The Matching Lattice and its Bases PoCo 2015 Summer School on Polyhedral Combinatorics
e∈F x(e). M denotes the set of all perfect matchings of G. χ denotes the incidence vector of M . Cuts: A cut of G is a subset of E that is the coboundary ∂(S) of some subset S of V . For a cut C := ∂(S), S and S are the shores of C. A cut is trivial if one of its shores is a singleton. A cut is odd if both its shores have odd cardinality. Note: This is the notation used in Bondy and Murty’s boo...
متن کاملSão Paulo School of Advanced Science on Algorithms, Combinatorics and Optimization The Perfect Matching Polytope, Solid Bricks and the Perfect Matching Lattice
e∈F x(e). M denotes the set of all perfect matchings of G. χ denotes the incidence vector of M . Cuts: A cut of G is a subset of E that is the coboundary ∂(S) of some subset S of V . For a cut C := ∂(S), S and S are the shores of C. A cut is trivial if one of its shores is a singleton. A cut is odd if both its shores have odd cardinality. Note: This is the notation used in Bondy and Murty’s boo...
متن کاملCsc5160: Combinatorial Optimization and Approximation Algorithms Topic: Perfect Matching Polytope 12.1 Formulation of General Perfect Matching
In this lecture, the focus is on general perfect matching problem where the goal is to prove that it can be solved in polynomial time by linear programming. Based on the LP formulation for bipartite matching studied in Lecture 10, we add some valid inequalities to establish a new formulation. Then we prove that for general perfect matching, all vertex solutions of the linear program are integra...
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An Euler brick is a cuboid with integer side dimensions such that the face diagonals are integers. Already in 1740, families of Euler bricks have been found. Euler himself constructed more families. If the space diagonal of an Euler brick is an integer too, an Euler brick is called a perfect Euler brick. Nobody has found one. There might be none. Nevertheless, it is an entertaining sport to go ...
متن کاملEstablishing the Matching Polytope
This paper gives an elementary, inductive proof-" graphical " in spirit-of a theorem of Edmonds' which specifies the convex hull of the matchings of an arbitrary, finite, undirected graph in terms of a fmite system of linear inequalities.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2004
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2004.08.003