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

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

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...

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

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...

matroid of a graph of branchwidth two, so its minimal forbidden minors are the graphic matroid of K4 and the non-graphic matroid U(2,4). The matroids...

not affect the resulting graph H. Graph minors are often studied in the more general context of matroid minors. In this context, it is common to assume...

every finite field, the family of matroids that can be represented over that field has only finitely many excluded minors. A proof of the conjecture was...

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...

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 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 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...

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

graph minors, a family that is closed under minors always has a finite obstruction set. Erdős–Hajnal conjecture Forbidden subgraph problem Matroid minor Zarankiewicz...

undergraduate education Minor (graph theory), a relation of one graph to another Minor (matroid theory), a relation of one matroid to another Minor (linear algebra)...

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...

{\displaystyle F} . If a matroid is regular, so is its dual matroid, and so is every one of its minors. Every direct sum of regular matroids remains regular....

structure theory of matroids. Excluding the Fano plane as a matroid minor is necessary to characterize several important classes of matroids, such as regular...

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

configurations) appear in a characterization of the graphic matroids by forbidden matroid minors. Wagner, K. (1937), "Über eine Eigenschaft der ebenen Komplexe"...

components. Minors of the frame matroid agree with minors of the biased graph; that is, M(Ω−S) = M(Ω)−S and M(Ω/S) = M(Ω)/S. Frame matroids generalize...

hereditary property. For instance, a family that is closed under taking matroid minors may be called "hereditary". In planning and problem solving, or more...

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

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...

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...

Kapoor for the GF(4) case of Rota's conjecture on matroid minors. Bertrand Guenin for a forbidden minor characterization of the weakly bipartite graphs...

characteristic polynomial, making it a graph determined by its spectrum. Vámos matroid Weisstein, Eric W. "Diamond Graph". MathWorld. ISGCI: Information System...

fact, they have at most as many edges as they have vertices) – and their matroid structure allows several other families of sparse graphs to be decomposed...