In this Daper the concept of conflict graph associated with a pseudo-Boolean function is discussed; one exploits the fact that the problem of finding a stable set with maximum weight in a graph can be reduced to the maximisation of a pseudo-Boolean function and conversely. On these Boolean foundations a graph theoretical procedure is developed associating to any graph another one having a strictly smaller stability number. Fragmentary computational experience seems to show that this reduction may be applied efficiently in algorithms for obtaining the stability number of a graph.