Definition:Transitive Reduction/Relation Theory

Definition

Let $\RR$ be a relation on a set $S$.

A transitive reduction of $\RR$ is denoted $\RR^-$, and is defined as a minimal relation on $S$ which has the same transitive closure as $\RR$.

Also see

• Transitive Reduction Exists if Transitive Closure Antisymmetric and Finite

• Results about transitive reductions can be found here.