For the purpose of large scale computing, we are interested in linking computers into large interconnection networks. In order for these networks to be useful, the underlying graph must possess desirable properties such as a large number of vertices, high connectivity and small diameter. In this paper, we are interested in the alternating group graph, as an interconnection network, and the k-Disjoint Path Problem. We give a proof that the alternating group graph, An, has the (n− 2)-Disjoint Path Property. We close with a discussion on possible research stemming from this work.