In mathematics, a uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer...

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

theory of matroids, the rank of a matroid is the maximum size of an independent set in the matroid. The rank of a subset S of elements of the matroid is, similarly...

In the mathematical theory of matroids, a graphic matroid (also called a cycle matroid or polygon matroid) is a matroid whose independent sets are the...

theory of matroids, a matroid representation is a family of vectors whose linear independence relation is the same as that of a given matroid. Matroid representations...

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...

In mathematics, a bipartite matroid is a matroid all of whose circuits have even size. A uniform matroid U n r {\displaystyle U{}_{n}^{r}} is bipartite...

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

free matroid over a given ground-set E is the matroid in which the independent sets are all subsets of E. It is a special case of a uniform matroid; specifically...

In matroid theory, the dual of a matroid M {\displaystyle M} is another matroid M ∗ {\displaystyle M^{\ast }} that has the same elements as M {\displaystyle...

In matroid theory, an Eulerian matroid is a matroid whose elements can be partitioned into a collection of disjoint circuits. In a uniform matroid U n...

In matroid theory, a field within mathematics, a gammoid is a certain kind of matroid, describing sets of vertices that can be reached by vertex-disjoint...

a matroid polytope, also called a matroid basis polytope (or basis matroid polytope) to distinguish it from other polytopes derived from a matroid, is...

Hence, the concept of basis of a matroid generalizes the concept of basis from linear algebra. In a uniform matroid, where the independent sets are all...

mathematical theory of matroids, a paving matroid is a matroid in which every circuit has size at least as large as the matroid's rank. In a matroid of rank r {\displaystyle...

of matroids, a minor of a matroid M is another matroid N that is obtained from M by a sequence of restriction and contraction operations. Matroid minors...

In mathematics, a regular matroid is a matroid that can be represented over all fields. A matroid is defined to be a family of subsets of a finite set...

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

sets of a matroid. For example, every bundle must contain at most k items, where k is a fixed integer (this corresponds to a uniform matroid). Or, the...

is the uniform matroid U(2,3), the graphic matroid of the triangle graph. A matroid has branchwidth two if and only if it is the graphic matroid of a graph...

matroid theory, a binary matroid is a matroid that can be represented over the finite field GF(2). That is, up to isomorphism, they are the matroids whose...

downwards-closed non-matroid constraint. The approximation factors obtainable by an SPM are naturally better: Uniform matroid, partition matroid - e/(e-1) ≅ 1...

\lambda } the weight of the largest element in an optimal basis in a uniform matroid, and Dey showed that his O ( n k 1 / 3 ) {\displaystyle O(nk^{1/3})}...

A sparsity matroid is a mathematical structure that captures how densely a multigraph is populated with edges. To unpack this a little, sparsity is a...

matroid. In the n {\displaystyle n} -point line (i.e., the rank 2 uniform matroid on n {\displaystyle n} elements, U n 2 {\displaystyle U{}_{n}^{2}}...

matrix whose columns are the v i {\displaystyle v_{i}} . Then the vector matroid M _ {\displaystyle {\underline {\mathcal {M}}}} on the columns of M {\displaystyle...

Configurations Line arrangements Hyperplane arrangements Buildings An oriented matroid is a mathematical structure that abstracts the properties of directed graphs...

combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid. The problem was formulated...

hypersimplex Δ d , k {\displaystyle \Delta _{d,k}} is also the matroid polytope for a uniform matroid with d {\displaystyle d} elements and rank k {\displaystyle...

dimension of the cycle space of a graph, in terms of matroid theory as the corank of a graphic matroid, and in terms of topology as one of the Betti numbers...