Definition:Cycle Matroid

Definition
Let $G$ be a graph.

Let $E$ be the edge set of $G$.

Let $\mathscr I$ be the set of edge sets of subgraphs of $G$ that contain no cycles.

Then the ordered pair $\struct{E, \mathscr I}$ is called the cycle matroid of the graph $G$.

Also see

 * Leigh.Samphier/Sandbox/Cycle Matroid is Matroid