The dominating set problem is fixed parameter tractable for graphs of bounded genus

We describe an algorithm for the dominating set problem with time complexity O((4g+40)kn2) for graphs of bounded genus g ≥ 1, where k is the size of the set. It has previously been shown that this problem is fixed parameter tractable for planar graphs. We give a simpler proof for the previous O(8kn2) result for planar graphs. Our method is a refinement of the earlier techniques.

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