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

duality extends to binary matroids: a binary matroid is Eulerian if and only if its dual matroid is a bipartite matroid, a matroid in which every circuit...

duality extends 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...

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...

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 uniform matroid is a matroid in which the independent sets are exactly the sets containing at most r elements, for some fixed integer...

proved that the binary matroids (matroids representable over the field of two elements) have a single forbidden minor, the uniform matroid U 4 2 {\displaystyle...

to binary matroids (which include the graphic matroids derived from planar graphs): a binary matroid is Eulerian if and only if its dual matroid is bipartite...

generally among the binary matroids, the bipartite matroids (matroids in which every circuit is even) are dual to the Eulerian matroids (matroids that can be...

regular matroids, about which he proved deep results. In addition, Tutte developed an algorithm for determining whether a given binary matroid is a graphic...

In mathematics, a regular matroid is a matroid that can be represented over all fields. A matroid is defined to be a family of subsets of a finite set...

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 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...

of 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...

of a relation is the smallest equivalence relation that contains it. In matroid theory, the closure of X is the largest superset of X that has the same...

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...

Branch-decompositions and branchwidth may also be generalized from graphs to matroids. An unrooted binary tree is a connected undirected graph with no cycles in which...

mathematician Alfred Lehman showed that Hex cannot be represented as a binary matroid, so a determinate winning strategy like that for the Shannon switching...

Thus the combinatorial topics may be enumerative in nature or involve matroids, polytopes, partially ordered sets, or finite geometries. On the algebraic...

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

sets of a matroid. For example, every bundle must contain at most k items, where k is a fixed integer (this corresponds to a uniform matroid). Or, the...

nodes, 68 different degree sequences of four-node connected graphs, and 68 matroids on four labeled elements. Størmer's theorem proves that, for every number...

vector. Matroid rank functions Let Ω = { e 1 , e 2 , … , e n } {\displaystyle \Omega =\{e_{1},e_{2},\dots ,e_{n}\}} be the ground set on which a matroid is...

programming Odds algorithm used to solve optimal stopping problems Oriented matroid Quadratic programming, a superset of linear programming Semidefinite programming...

a two-edge path) but the graphic matroid formed by this bridge is not connected, so no circuit of the graphic matroid of K 2 , 3 {\displaystyle K_{2,3}}...

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

University. Her dissertation, Minors of 3-Connected Matroids and Adjoints of Binary Matroids, concerned matroid theory and was supervised by Robert E. Bixby...

6. Independence theory 7.6.1. Independence structures 7.6.2. Efficient matroid algorithms 7.7. Discrete dynamic programming (see also transfer-matrix...