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...

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...

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

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

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...

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...

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...

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

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...

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...

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

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 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...

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 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...

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

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

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...

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...

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...

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...

may be partitioned into categories, and each bundle must contain at most kc items from each category c (this corresponds to a partition matroid). In general...

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...

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...

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...