Computing simple-path convex hulls in hypergraphs

a r t i c l e i n f o a b s t r a c t Keywords: Graph algorithms Simple-path convexity Simple-path convex hull Totally balanced 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.