A characterization of solvability for a class of networks

In this paper,we find that Property P can be generalized to characterize the solvability of a kind of networks with any number of sources,thus partially answering the open problem as to whether there are properties similar to Property P to characterize the solvability of some networks.As an application,for a given integer n,we construct such a solvable network that has no solvable solution if its alphabet size is less than n.