This paper considers distributed vertex-coloring in broadcast/receive networks suffering from conflicts and collisions. (A collision occurs when, during the same round, messages are sent to the same process by too many neighbors; a conflict occurs when a process and one of its neighbors broadcast during the same round.) More specifically, the paper focuses on multi-channel networks, in which a process may either broadcast a message to its neighbors or receive a message from at most γ of them. The paper first provides a new upper bound on the corresponding graph coloring problem (known as frugal coloring) in general graphs; proposes an exact bound for the problem in trees; presents a deterministic, parallel, color-optimal, collision-and conflict-free distributed coloring algorithm for trees; proves the correctness of this algorithm; and finally evaluates experimentally its performance using simulations that show our solution clearly outperforms a reference protocol for distributed TDMA slot-allocation.