In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges...

p. 337). We have R+ = R if, and only if, R itself is transitive. Conversely, transitive reduction adduces a minimal relation S from a given relation R...

contains a longer directed path from u to v. Like the transitive closure, the transitive reduction is uniquely defined for DAGs. In contrast, for a directed...

In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates...

a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ( S , ≤ ) {\displaystyle...

{\displaystyle G=(S,T)} with T ⊆ R {\displaystyle T\subseteq R} the transitive reduction of R. For example, assume a simple calculator. This calculator supports...

directed consistently downwards. For a partial ordering given by its transitive reduction (covering relation), the Coffman–Graham algorithm can be implemented...

for which x ≤ y. An alternative way of doing this is to use the transitive reduction of the partial ordering; in general, this produces DAGs with fewer...

networks Spectral graph theory Strongly regular graphs Symmetric graphs Transitive reduction Tree data structure Bellman–Ford algorithm Borůvka's algorithm Breadth-first...

node and each element of < {\displaystyle <} to be an edge. The transitive reduction of this DAG is then the Hasse diagram. Similarly this process can...