<p>In a digraph D = (X, U), not necessarily finite, an arc (x, y) âˆˆ U is reachable from a vertex u if there exists a directed walk W that originates from u and contains (x, y). A subset S âŠ† X is an arc-reaching set of D if for every arc (x, y) there exists a diwalk W originating at a vertex u âˆˆ S and containing (x, y). A minimal arc-reaching set is an arc-basis. S is a point-reaching set if for every vertex v there exists a diwalk W to v originating at a vertex u âˆˆ S. A minimal point-reaching set is a point-basis. A study of hypergraphs formed by minimal arc bases of a digraph is the main objective of this paper.</p>
B. D. Acharya, Abhishek, K., and Germina, K. A., “Hypergraphs of Minimal Arc Bases in A Digraph”, Journal of Combinatorics & System Sciences, vol. 37, no. 2-4, pp. 307-319, 2012.