Unexpected behaviour of crossing sequences

  title={Unexpected behaviour of crossing sequences},
  author={Matt DeVos and Bojan Mohar and Robert S{\'a}mal},
  journal={J. Comb. Theory, Ser. B},
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.