Sur les coloriages stables des graphes booliens exclusifs

Authors :: Christine Decaestecker
Source :: Périodiques Scientifiques en Édition Électronique.
Publication Year :: 1985
Publisher :: Bruxelles : Académie Royale de Belgique, 1985.
Abstract: This paper proves that in any boolean graph, the determination of the stable states reduces to the classical determination of the stable sets of the underlying pure graph. For this purpose use is made of exclusive graphs : that is boolean graph in which all the vertices are NOR. To be more specific : it is proved that a coloured exclusive graph is stable if and only if the starting points of its red arrows (that is the arrows of value 1) constitute a stable set of the extended graph obtained in equipping all red arrows with a starting point (original or new).<br />Decaestecker Christine. Sur les coloriages stables des graphes booliens exclusifs . In: Bulletin de la Classe des sciences, tome 71, 1985. pp. 297-300.