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In this paper, we consider a point-to-point communication network of discrete memoryless channels. In the network, there are a source node and possibly more than one sink node. Information is generated at the source node and is multicast to each sink node. We allow a node to encode its received information before loading it onto an outgoing channel, where the channels are independent of each other. We also allow the nodes to pass along messages asynchronously. In this paper, we characterize the admissibility of single-source multi-sink communication networks. Our result can be regarded as a network generalization of Shannon's result that feedback does not increase the capacity of a discrete memoryless channels (DMCs), and it implies a separation theorem for network coding and channel coding in such a communication network.