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 ≥ n1+ε edges, has a subgraph G of at most (1 − δ)m edges and crossing number at least (1 − ε)cr(G). This generalizes the result of J. Fox and Cs. T´oth.

• Type: Conference
• Year: 2007
• Where: GD
• Authors: Jakub Cerný, Jan Kyncl, Géza Tóth
• Keywords: Computer Graphics, Continuous Fashion, GD 2007