Matroid partitioning is a problem arising in the mathematical study of matroids and in the design and analysis of algorithms. Its goal is to partition...

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

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...

The matroid intersection theorem, due to Jack Edmonds, says that there is always a simple upper bound certificate, consisting of a partitioning of the...

of a matroid. The matroid partitioning problem is to partition the elements of a matroid into as few independent sets as possible, and the matroid packing...

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...

Feshbach–Fano partitioning Foliation Frequency partition Graph partition Kernel of a function Lamination (topology) Matroid partitioning Multipartition...

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

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...

Balanced number partitioning is a variant of multiway number partitioning in which there are constraints on the number of items allocated to each set...

to binary matroids: a binary matroid is bipartite if and only if its dual matroid is an Eulerian matroid, a matroid that can be partitioned into disjoint...

special case of a more general matroid partitioning problem, in which one wishes to express a set of elements of a matroid as a union of a small number...

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...

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...

each connecting the distinguished vertices, can be represented as a matroid partitioning problem, which can be solved in polynomial time. Alternatively, it...

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...

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...

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...

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

are two matroids associated with a signed graph, called the signed-graphic matroid (also called the frame matroid or sometimes bias matroid) and the...

Graphic matroids and partition matroids are special cases of linear matroids. In the matroid parity problem, the input consists of a matroid together...

Intersection of two partition matroids - 6.75 Intersection of a graphic matroid and a partition matroid - 10.66 General matroid with matroid rank k {\displaystyle...

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...

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...

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...

of the matroid at its leaves. An e-separation may be defined in the same way as for graphs, and results in a partition of the set M of matroid elements...

mathematics, a base-orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. For any two bases A {\displaystyle...

matroid of M. Then Whitney's planarity criterion can be rephrased as stating that the dual matroid of a graphic matroid M is itself a graphic matroid...

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...

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...