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Judiciously assigning channels to a wireless mesh network can substantially enhance capacity of the network. One particular flavor of mesh network is that with a tree topology, which has the property that all traffic passes through one central point. Usually the allocation problem is linked to problems of routing, load, and measurements of interference. In this paper we take advantage of the restrictions on the routing, and on potential load imposed by the topology, to present an allocation algorithm that is tailored for wireless trees. Using the connection characteristics of the topology, we define a conflict graph over which a coloring heuristic can provide better performance by not having to focus on connectivity/routing/interference. We show that the algorithm has a low complexity (quadratic in the number of nodes), and in simulation shows significant gains in performance when compared to simpler solutions.