Crossing stars in topological graphs

Authors:
Gábor Tardos;Géza Tóth
Affiliations:
Rényi Institute, Hungarian Academy of Sciences, Budapest, Hungary;Rényi Institute, Hungarian Academy of Sciences, Budapest, Hungary
Venue:
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
Year:
2004

Citing 4
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Graphs and Combinatorics

Note: On the maximum number of edges in quasi-planar graphs

Journal of Combinatorial Theory Series A

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Abstract

Let G be a graph without loops or multiple edges drawn in the plane. It is shown that, for any k, if G has at least Ckn edges and n vertices, then it contains three sets of k edges, such that every edge in any of the sets crosses all edges in the other two sets. Furthermore, two of the three sets can be chosen such that all k edges in the set have a common vertex.