On the complexity of testing membership in the core of min-cost spanning tree games

LetN = {1,...,n} be a finite set of players andKN the complete graph on the node setN∪{0}. Assume that the edges ofKN have nonnegative weights and associate with each coalitionS∪N of players as costc(S) the weight of a minimal spanning tree on the node setS∪{0}.Using transformation from EXACT COVER BY 3-SETS, we exhibit the following problem to beNP-complete. Given the vectorxεℜitN withx(N) =c(N). decide whether there exists a coalitionS such thatx(S) >c(S).