This document discusses deadlock prevention in adaptive wormhole routing on k-ary n-cube interconnection networks. It examines two planar-adaptive routing schemes: the Turn Model and Chien and Kim's partially adaptive routing algorithm. The Turn Model restricts certain turns to ensure deadlock freedom using only two virtual channels regardless of network size. Chien and Kim's algorithm uses increasing and decreasing virtual networks to guarantee deadlock freedom using a fixed number of virtual channels that is independent of network dimensions. Both schemes allow for adaptive routing while preventing deadlock more cost-effectively than fully adaptive approaches.