Definition:Fundamental Circuit (Matroid)
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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