Jul 23, 2016
A string graph is the intersection graph of continuous arcs in the plane. Matoušek showed that every string graph with m edges has a balanced separator with O(√m . log(m)) vertices. Fox and Pach have conjectured that the correct bound is O(√m). and this would be optimal if true. We modify Jirka's argument to confirm their conjecture.
International Conference on The Mathematics of Jiří Matoušek, Charles University, Prague 2016
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