Improvement on the Decay of Crossing Numbers
We prove that the crossing number of a graph decays in a “continuous fashion” in the following sense. For any ε> 0 there is a δ> 0 such that for n sufficiently large, every graph G with n vertices and m ≥ n 1 + ε edges has a subgraph G′ of at most (1 − δ)m edges and crossing number at least Open image in new window . This generalizes the result of J. Fox and Cs. Tóth.
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