Researchers showed that on planar graphs the semitotal domination problem—where a set of vertices must dominate the graph and every vertex in the set must have another selected vertex within distance two—admits a linear‑size kernel. The kernel contains at most 358 times the parameter k, the requested size of the dominating set. The construction is achieved by repeatedly applying three polynomial‑time reduction rules that simplify the graph while preserving the optimum size. After exhaustive application the total number of vertices is bounded by 87·(3k–6)+97·k, which is always less than 358k; otherwise the instance is rejected as a no‑instance. The overall algorithm takes polynomial time, with an upper bound of O(n³). These results extend the toolkit of linear kernels known for domination‑type problems on planar graphs.