the matroid intersection problem is to find a largest common independent set in two matroids over the same ground set. If the elements of the matroid are...

In mathematics, a partition matroid or partitional matroid is a matroid that is a direct sum of uniform matroids. It is defined over a base set in which...

delta-matroid or Δ-matroid is a family of sets obeying an exchange axiom generalizing an axiom of matroids. A non-empty family of sets is a delta-matroid if...

In combinatorics, a matroid /ˈmeɪtrɔɪd/ is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many...

generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Matroid parity can be solved in polynomial...

proved the matroid intersection theorem, a very general combinatorial min-max theorem which, in modern terms, showed that the matroid intersection problem...

mathematics and computer science, a matroid oracle is a subroutine through which an algorithm may access a matroid, an abstract combinatorial structure...

An oriented matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane...

constraints can be done in polynomial time, by reduction to the weighted matroid intersection problem. Gross-substitute utilities are more general than additive...

matroid (and has the same relationship to the intersection semilattice as does the matroid to the lattice in the lattice case), but is not a matroid if...

Matroid-constrained number partitioning is a variant of the multiway number partitioning problem, in which the subsets in the partition should be independent...

and to compute the largest common independent set in the intersection of two given matroids. The arboricity of an undirected graph is the minimum number...

and the flat generated by a set T of elements is the intersection of L with the field K[T]. A matroid that can be generated in this way is called algebraic...

In mathematics, the Vámos matroid or Vámos cube is a matroid over a set of eight elements that cannot be represented as a matrix over any field. It is...

In the mathematics of matroids and lattices, a geometric lattice is a finite atomistic semimodular lattice, and a matroid lattice is an atomistic semimodular...

a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs...

{\displaystyle T} of elements is the intersection of L {\displaystyle L} with the field K [ T ] {\displaystyle K[T]} . A matroid that can be generated in this...

Not only the structure but also enumerative properties belong to matroid theory. Matroid theory was introduced by Hassler Whitney and studied as a part...

2-coloring and 3-coloring for graphs, in the matroid intersection problem for intersections of two or three matroids, and in 2-SAT and 3-SAT for satisfiability...

- 3 Intersection of two partition matroids - 6.75 Intersection of a graphic matroid and a partition matroid - 10.66 General matroid with matroid rank...

In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent...

problems that includes as special cases the minimum-cost flow problem, matroid intersection, and the problem of computing a minimum-weight dijoin in a weighted...

matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid....

efficient graph algorithms. They may also be generalized from graphs to matroids. Several important classes of graphs may be characterized as the graphs...

geometric lattices and matroids, this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms...

fact, they have at most as many edges as they have vertices) – and their matroid structure allows several other families of sparse graphs to be decomposed...

every clique of the underlying graph Partition matroid, a kind of matroid whose matroid intersections may form clique complexes Bandelt & Chepoi (2008)...

polyhedra, it is by now also capable of dealing with simplicial complexes, matroids, polyhedral fans, graphs, tropical objects, toric varieties and other objects...

oriented matroid with n {\displaystyle n} elements has at least 3 n / 7 {\displaystyle 3n/7} two-point lines, or equivalently every rank-3 matroid with fewer...

finite sets form the basis sets of a matroid, the transversal matroid of C. The independent sets of the transversal matroid are the partial transversals of...