Abstract
The 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 |−2 h−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.
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