Improvement on the decay of crossing numbers
Combinatorics
2013-08-07 v1 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1201.5421,
title = {Improvement on the decay of crossing numbers},
author = {Jakub Černý and Jan Kynčl and Géza Tóth},
journal= {arXiv preprint arXiv:1201.5421},
year = {2013}
}
Comments
7 pages, 1 figure