Sur les arborescences dans un graphe oriente

AbstractThe main result of this paper is the following theorem: Let G = (X,E) be a digraph without loops or multiple edges, |X| ⩾3, and h be an integer ⩾1, if G contains a spanning arborescence and if d+G(x)+d−G(x)+d−G(y)+d−G(y)⩾ 2|X |−2h−1 for all x, y ϵ X, x ≠ y, non adjacent in G, then G contains a spanning arborescence with ⩽h terminal vertices. A strengthening of Gallai-Milgram's theorem is also proved