acyclic digraph

English

Noun

acyclic digraph (plural acyclic digraphs)

1. (graph theory, computer science) A directed acyclic graph, a finite directed graph that contains no directed cycles.
   • 1993, Suh-Ryung-Kim, The Competition Number and Its Variants, J. Gimbel, J.W. Kennedy, L.V. Quintas (editors), Quo Vadis, Graph Theory?: A Source Book for Challenges and Directions, Elsevier (North-Holland), page 313,

     In the study of the competition graph of an acyclic digraph, there are two fundamental questions which were proposed by Roberts in 1978: One is to characterize the acyclic digraphs that have interval competition graphs and the other is to characterize the graphs which are competition graphs of acyclic digraphs.

   • 2009, Tamara Mchedlidze, Antonios Symvonis, Crossing-Optimal Acyclic HP-Completion for Outerplanar st-Digraphs, Hung Q. Ngo (editor), Computing and Combinatorics: 15th Annual International Conference, Proceedings, Springer, LNCS 5609, page 76,

     Determining whether a graph has a hamiltonian path or circuit is NP-complete [3]. The problem remains NP-complete for cubic planar graphs [3], for maximal planar graphs [9], and for planar digraphs [3]. It can be trivially solved in polynomial time for planar acyclic digraphs.

   • 2018, Gregory Gutin, 3. Acyclic Digraphs, Jørgen Bang-Jensen, Gregory Gutin, Classes of Directed Graphs, Springer, page 125,

     Acyclic digraphs form a well-studied family of digraphs of great interest in graph theory, algorithms and applications.

Synonyms

• (directed graph without cycles): acyclic directed graph, directed acyclic graph (DAG)

Translations

directed acyclic graph — see directed acyclic graph