Improvement on the decay of crossing numbers

Authors:
Jakub Černý;Jan Kynčl;Géza Tóth
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 1, Czech Republic;Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Praha 1, Czech Republic;Rényi Institute, Hungarian Academy of Sciences, Budapest, Hungary
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

Citing 3
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Abstract

We prove that the crossing number of a graph decays in a "continuous fashion" in the following sense. For any Ɛ 0 there is a Ɛ 0 such that for n sufficiently large, every graph G with n vertices and m ≥ n1+Ɛ edges has a subgraph G' of at most (1 - δ)m edges and crossing number at least (1 - Ɛ)cr(G). This generalizes the result of J. Fox and Cs. Tóth.