Toppling kings in multipartite tournaments by introducing new kings

摘要

Let t=(t_1,t_2,...,t_n) and c=(c _1,c_2,...,c_n) be two n-tuples of nonnegative integers. An all-4-kings n-partite tournament T(V_1,V _2,...V_n) is said to have a (t,c)-property if there exists an n-partite tournament T_1(W_1,W_2,...,W _n) such that for each i∈1,...,n: (1)V_i?W _i; (2) exactly t_i 4-kings of V_i are not 4-kings in T_1; (3) exactly c_i 4-kings of W_i are not vertices of V_i. We describe all pairs (t,c) such that there exists an n-partite tournament having (t,c)-property.