Cycle matroid

Cycle matroid --- матроид циклов.

Let [math]\displaystyle{ E(G) }[/math] be the edge-set of a graph [math]\displaystyle{ G }[/math] and [math]\displaystyle{ C }[/math] be the set of cycles. The cycles satisfy the circuit postulates. Thus, we obtain a matroid related to the graph. We denote this matroid by [math]\displaystyle{ M(G) }[/math] and call it the cycle matroid of [math]\displaystyle{ G }[/math]. The bases of [math]\displaystyle{ M(G) }[/math] are the spanning trees.

The rank of [math]\displaystyle{ M(G) }[/math] is less by 1 than the number of vertices.