P1: the union of all {Xi, i in I, equals to V;
P2: for every edge (v, w) in E, the is an i in I such that v and w are in Xi;
P3: for every i, j and k in I, if j is in a path between i and k in T, then the intersection of Xi and Xk is contained in Xj.
wikipedia.org dumped 2003-03-17 with terodump