Definition:Parallel (Matroid)
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This page is about Parallel in the context of Matroid Theory. For other uses, see Parallel.
Definition
Let $M = \struct {S, \mathscr I}$ be a matroid.
Two elements $x, y \in S$ are said to be parallel in $M$ if and only if they are not loops but $\set {x, y}$ is a dependent subset of $S$.
That is, $x, y \in S$ are parallel if and only if:
- $\set x, \set y \in \mathscr I$ and $\set {x, y} \notin \mathscr I$.
Sources
- 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 4.$ Loops and parallel elements