Sur les arborescences dans un graphe oriente |
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Authors: | Michel Las Vergnas |
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Institution: | C.N.R.S., Paris, France |
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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 |?2h?1 for all x, y?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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