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Time division multiple access (TDMA) is a method for sharing communication media. In wireless communications, TDMA algorithms often divide the radio time into timeslots of uniform size, ξ, and then combine them into frames of uniform size, b τ. We consider TDMA algorithms that allocate at least one timeslot in every frame to every node. Given a maximal node degree, δ, and no access to external references for collision detection, time or position, we consider the problem of collision-free self-stabilizing TDMA algorithms that use constant frame size. We demonstrate that this problem has no solution when the frame size is τ <; max{2δ, χ ₂ }, where χ ₂ is the chromatic number for distance-2 vertex coloring. As a complement to this lower bound, we focus on proving the existence of collision-free self-stabilizing TDMA algorithms that use constant frame size of τ. We consider basic settings (no hardware support for …