In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that if there is a directed path from vertex u to vertex v and v comes before u in the ordering, then there is also a directed path from vertex v to vertex u.
If the graph is a directed acyclic graph (DAG), topological orderings are pre-topological orderings and vice versa. In other cases, any pre-topological ordering gives a partial order.
- ^ a b Schrijver, Alexander (2002-12-10). Combinatorial Optimization: Polyhedra and Efficiency. Springer Science & Business Media. p. 89. ISBN 9783540443896.
- ^ Sedgewick, Robert; Wayne, Kevin (2016-09-26). "Directed Graphs". Algorithms, 4th Edition. Retrieved 2017-09-06.