Literature is plentiful in works exploiting cache locality for GPUs. A majority of them explore replacement or bypassing policies. In this paper, however, we surpass this exploration by fabricating a formal proof for a no-overhead quasi-optimal caching technique for caching textures in graphics workloads. Textures make up a significant part of main memory traffic in mobile GPUs, which contributes to the total GPU energy consumption. Since texture accesses use a shared L2 cache, improving the L2 texture caching efficiency would decrease main memory traffic, thus improving energy efficiency, which is crucial for mobile GPUs. Our proposal reaches quasi-optimality by exploiting the frame-to-frame reuse of textures in graphics. We do this by traversing frames in a boustrophedonic 1 manner w.r.t. the frame-to-frame tile order. We first approximate the texture access trace to a circular trace and then forge a formal proof for our proposal being optimal for such traces. We also complement the proof with empirical data that demonstrates the quasi-optimality of our no-cost proposal.