Definition:Loop (Matroid)

This page is about Loop in the context of Matroid Theory. For other uses, see Loop.

Definition

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

A loop of $M$ is an element $x$ of $S$ such that $\set x$ is a dependent subset of $S$.

That is, $x \in S$ is a loop if and only if $\set x \not \in \mathscr I$.

Sources

• 1976: Dominic Welsh: Matroid Theory ... (previous) ... (next) Chapter $1.$ $\S 4.$ Loops and parallel elements