Computing simple-path convex hulls in hypergraphs

In a connected hypergraph a vertex set X is simple-path convex (sp-convex, for short) if either |X|=<1 or X contains every vertex on every simple path between two vertices in X (Faber and Jamison, 1986 [7]), and the sp-convex hull of a vertex set X is the minimal superset of X that is sp-convex. In this paper, we give a polynomial algorithm to compute sp-convex hulls in an arbitrary hypergraph.