Matroid: circuit

Dependencies:

1. Matroid

Let $M = (S, I)$ be a matroid. Then $C \subseteq S$ is said to be a circuit iff both these conditions hold:

• Dependence: $C \not\in I$
• Minimality: $\forall x \in C, C - x \in I$. Equivalently, every proper subset of $C$ is independent.

A circuit of size 1 is called a loop.

Dependency for:

1. Matroid: dependent iff has circuit
2. Matroid: non-disjoint circuits
3. Matroid: unique circuit

Info:

• Depth: 1
• Number of transitive dependencies: 1

Transitive dependencies:

1. Matroid