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Near-optimal separators in string graphs
Published 26 Feb 2013 in math.CO, cs.DM, and cs.DS | (1302.6482v2)
Abstract: Let G be a string graph (an intersection graph of continuous arcs in the plane) with m edges. Fox and Pach proved that G has a separator consisting of O(m{3/4}\sqrt{log m})$ vertices, and they conjectured that the bound of O(\sqrt m) actually holds. We obtain separators with O(\sqrt m \log m) vertices.
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