Meaning of acyclic digraph | Babel Free

Definitions

A directed acyclic graph, a finite directed graph that contains no directed cycles.

Examples

“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.”

CEFR level