=. ,

=. ,

=. ,

G. Est, De plus, le sous-graphe induit par A 2 ? A 4 est le double biparti de G (i.e. un graphe biparti constitué de deux copies de G dont les arêtes correspondentàcorrespondentà celles de G), tandis que A 2 ? A 5 est le double biparti de G augmenté d'un couplage. On a bien G ? biparti chacun des A i ´ etant un stable.-Si (G, k) est une instance positive de Degré minimum par complémentation locale il existe un sous ensemble de sommets D ? V (G) tel que D = ? et |D ? Odd G (D)| ? k + 1

D. Donc and ?. Fait-de-(g-?-,-k,

(. Si, est une instance positive de Ensemble pair il existe D ? A 1 ? A 2 ? A 3 tel que |D| ? k ? et Odd G ? (D) = ?

, Degré minimum par complémentation locale appartientà appartientà

, CetétatCetétat de fait contraste avec la classe desprobì emeséquivalentsàemeséquivalentsemeséquivalentsà Ensemble impair qui appartiennent aussì a W [2] mais qui en plus sont difficiles pour W [1] [11], cette classe contenant d'autresprobì emes liés auxétatsauxétats-graphes comme Plus grand ensemble WOD et Seuil quantique, vol.11

, Remerciments Je remercie mes ma??tresma??tres de thèse Pablo Arrighi et Simon Perdrix ainsi que

, Je tiens aussì a remercier Laurent Besacier, Christian Boitet et Rachid Echahed qui m'ont apporté aide et soutien durant ma thèse. Enfin je remercie Spin et Anne-So pour avoir relu ma thèse ainsi que mes parents pour leur soutien, Mehdi Mhalla pour m'avoir guidé tout au long de ma thèse

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