Near-optimal separators in string graphs

Jiri Matousek

Published 2013-02-26, updated 2013-05-06Version 2

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.