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Near-Optimal Separators in String Graphs
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- Journal:
- Combinatorics, Probability and Computing / Volume 23 / Issue 1 / January 2014
- Published online by Cambridge University Press:
- 07 October 2013, pp. 135-139
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- Article
- Export citation
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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.
