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

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...

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

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...

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...

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 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...

Matroid, Inc. is a computer vision company that offers a platform for creating computer vision models, called detectors, to search visual media for objects...

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...

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...

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

In mathematics, a colored matroid is a matroid whose elements are labeled from a set of colors, which can be any set that suits the purpose, for instance...

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...

In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence....

In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is...

accomplishments, including foundation work in the fields of graph theory and matroid theory. Tutte's research in the field of graph theory proved to be of remarkable...

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...

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

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 the mathematics of structural rigidity, a rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with...

In the mathematical subject of matroid theory, the bicircular matroid of a graph G is the matroid B(G) whose points are the edges of G and whose independent...

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...

B is unbalanced. Biased graphs are interesting mostly because of their matroids, but also because of their connection with multiary quasigroups. See below...

In combinatorics, a matroid embedding is a set system (F, E), where F is a collection of feasible sets, that satisfies the following properties. Accessibility...

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 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...

machine learning. He is adjunct professor at Stanford University, CEO of Matroid, and a founding team member at Databricks. His work focuses on machine...

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, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids correspond...

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...