一个人员指派问题(英文)

Let T be a set of personnel.Suppose that“≤”is a partial ordering relationon T(which expresses,for example,the seniority of the perssonnel)such that(T,≤)is a rooted tree.Let U be a subset of T.If U can be partitioned into groups eachconsisting of one leader,say t,and k ordinary members,say t_1,t_2,…,t_k,with theproperty that the leader must have higher seniority than the k ordinary members,