D. Si, Pour chaque ar^ ete (u, v) en pointillé qui est un isthme de G faire 9. Basculer (u, v) en ar^ ete solide

D. Si, Pour chaque ar^ ete (u, v) en pointillé faire 12 Supprimer (u, v) de G si une des conditions suivante est vérifiée : 13 a, |C(v)| > 1, et C(u) = C(v)

.. Filtrer-la-contrainte-tree, 49 4.2.1 Existence d'une solution pour une contrainte tree 49 4.2.2 Arc-consistance généralisée pour la contrainte tree, Complexité, p.53

. Pour, Gprec tel que u = r(u) et v / ? CC (u) faire 5. remplacer (u, v)

. Pour, G maybe faire 10. supprimer (u, v) de G maybe si une des conditions suivante est vérifiée : 11. a. (CC (u), CC (v)) crée un circuit dans G H prec CC (v)) crée un arc transitif dans G H prec

F. Questions, nous conclurons cette thèse par une liste de questions et deprobì emes spécifiques rencontrés au cours de notré etude : ? L'´ evaluation d'une borne supérieure sur le nombre d'arbres propres (NPROP) pouvant couvrir un graphe orienté. Plus précisément, est-ce que l'´ evaluation de cette bornereì eve d'unprobì eme polynomial ou non ?

?. La-complexité-d, un algorithme de filtrage atteignant l'arc-consistance généralisée pour une contrainte d'arbre restreinte par un ensemble d'incomparabilités entre les sommets du graphè a partitionner

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