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...

cycle matroid. Matroids derived in this way are graphic matroids. Not every matroid is graphic, but all matroids on three elements are graphic. Every...

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...

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...

basis has a specialized name in several specialized kinds of matroids: In a graphic matroid, where the independent sets are the forests, the bases are called...

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...

structure from which the matroid was defined for graphic matroids, transversal matroids, gammoids, and linear matroids, and for matroids formed from these by...

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...

transversal matroid and a strict gammoid. Not every uniform matroid is graphic, and the uniform matroids provide the smallest example of a non-graphic matroid, U...

the lattice of partitions corresponds to the lattice of flats of the graphic matroid of the complete graph. Another example illustrates refinement of partitions...