Near-optimal separators in string graphs
Combinatorics
2013-05-07 v2 Discrete Mathematics
Data Structures and Algorithms
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.
Cite
@article{arxiv.1302.6482,
title = {Near-optimal separators in string graphs},
author = {Jiri Matousek},
journal= {arXiv preprint arXiv:1302.6482},
year = {2013}
}
Comments
4 pages; minor corrections and updates compared to version 1