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...

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...

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

graph: it is not planar but can be embedded in a torus, with each face of the embedding being a triangle. This embedding has the Heawood graph as its dual...

vector space). The image of that embedding is the Klein quadric in RP5. Hermann Grassmann generalized Plücker's embedding to arbitrary k and n. The homogeneous...

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

planar if and only if its graphic matroid is also cographic (that is, it is the dual matroid of another graphic matroid). In purely graph-theoretic terms...

rigidity matroid is a matroid that describes the number of degrees of freedom of an undirected graph with rigid edges of fixed lengths, embedded into Euclidean...

matroid is a matroid endowed with a function that assigns a weight to each element. Formally, let M = ( E , I ) {\displaystyle M=(E,I)} be a matroid,...

} In matroid theory, two particularly important special classes of matroids are the wheel matroids and the whirl matroids, both derived from...

edge. An embedding of maximum genus may be obtained from a planar embedding of the Xuong tree by adding each two-edge path to the embedding in such a...

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, 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...

graph theory, a mathematical discipline, a linkless embedding of an undirected graph is an embedding of the graph into three-dimensional Euclidean space...

oriented matroid with n {\displaystyle n} elements has at least 3 n / 7 {\displaystyle 3n/7} two-point lines, or equivalently every rank-3 matroid with fewer...

"non-Fano configuration", which can be embedded in the real plane. It is another important example in matroid theory, as it must be excluded for many...

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...

also be expressed using the theory of matroids, according to which a spanning tree is a base of the graphic matroid, a fundamental cycle is the unique circuit...

straight-line embedding of any planar graph into a grid of small area. The arboricity of a graph can be expressed as a special case of a more general matroid partitioning...

graph G {\displaystyle G} , and every planar embedding of G {\displaystyle G} , the faces of the embedding that are induced cycles must be peripheral cycles...

rigidity of rod-and-hinge linkages is described by a matroid. The bases of the two-dimensional rigidity matroid (the minimally rigid graphs in the plane) are...

matroid theory, the family of sets complementary to the independent sets of a given matroid themselves form another matroid, called the dual matroid....

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...

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

LYM inequality) Lucas chain MacMahon's master theorem Magic square Matroid embedding Monge array Monomial order Moreau's necklace-counting function Motzkin...

is provided by the graphs with linkless embeddings and knotless embeddings. A linkless embedding is an embedding of the graph with the property that any...

for important progress on regular matroids and totally unimodular matrices, the four colour theorem, linkless embeddings, graph minors and structure, the...

graphs to incrementally build planar embeddings of every 3-connected component of G (and hence a planar embedding of G itself). The construction starts...

he proved the matroid intersection theorem, a very general combinatorial min-max theorem which, in modern terms, showed that the matroid intersection problem...

Conway's definition, an n-tangle is a proper embedding of the disjoint union of n arcs into a 3-ball; the embedding must send the endpoints of the arcs to 2n...