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Near-Optimal Separators in String Graphs

Published online by Cambridge University Press:  07 October 2013

JIŘÍ MATOUŠEK
JIŘÍ MATOUŠEK*
Affiliation:
Department of Applied Mathematics and Institute of Theoretical Computer Science (ITI), Charles University, Malostranské nám. 25, 11800 Praha 1, Czech Republic and Institute of Theoretical Computer Science, ETH Zurich, 8092 Zurich, Switzerland (e-mail: matousek@kam.mff.cuni.cz)
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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.

Keywords

Primary 05C62Secondary 05C10
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 1 , January 2014 , pp. 135 - 139
Copyright
Copyright © Cambridge University Press 2013 

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