Definition:Fundamental Circuit (Matroid)

Definition

Let $M = \struct {S, \mathscr I}$ be a matroid.

Let $B$ be a base of $M$.

Let $x \in S \setminus B$.

The fundamental circuit of $x$ in the base $B$, denoted $\map C {x, B}$, is the unique circuit such that:

$x \in \map C {x, B} \subseteq B \cup \set x$

Also see

• Matroid Base Union External Element has Fundamental Circuit where it is proved that the fundamental circuit exists.

Sources

• 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 9.$ Circuits