Before revision:  We assume that U and (w_{u)_{u \in U} are }  known in advance, and that the patience, adjacent edges and edge probabilities for each \scr{C} online vertex are only revealed when the online vertex arrives.
After revision:  We assume that U )_{u \in U} are } known in advance, and that the patience, adjacent edges and edge probabilities for each \scr{C} online vertex are only revealed when the online vertex arrives.