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arXiv · 1201.5421

Improvement on the decay of crossing numbers

Jakub Černý·Jan Kynčl·Géza Tóth
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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 epsilon>0 there is a delta>0 such that for a sufficiently large n, every graph G with n vertices and m > n^{1+epsilon} edges, has a subgraph G' of at most (1-delta)m edges and crossing number at least (1-epsilon)cr(G). This generalizes the result of J. Fox and Cs. Toth.

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Jakub Černý, Jan Kynčl, Géza Tóth. 2012-01-26. Improvement on the decay of crossing numbers. https://doi.org/10.1007/s00373-012-1137-3

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