Highly Influenced

@article{DeVos2011UnexpectedBO, title={Unexpected behaviour of crossing sequences}, author={Matt DeVos and Bojan Mohar and Robert S{\'a}mal}, journal={J. Comb. Theory, Ser. B}, year={2011}, volume={101}, pages={448-463} }

- Published 2011 in J. Comb. Theory, Ser. B
DOI:10.1016/j.jctb.2010.12.002

The n crossing number of a graph G, denoted crn(G), is the minimum number of crossings in a drawing of G on an orientable surface of genus n. We prove that for every a > b > 0, there exists a graph G for which cr0(G) = a, cr1(G) = b, and cr2(G) = 0. This provides support for a conjecture of Archdeacon et al. and resolves a problem of Salazar.