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

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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...

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...

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...

{\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...

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

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...

definition of the span of points in space, a subset X of the ground set of a matroid is called a spanning set if the rank of X equals the rank of the entire...

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

In linear algebra and matroid theory, Rota's basis conjecture is an unproven conjecture concerning rearrangements of bases, named after Gian-Carlo Rota...

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...

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

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

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...