Abstrakt
The nth crossing number of a graph G, denoted cr(n)(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 cr(0)(G) = a, cr(1)(G) = b, and cr(2)(G) = 0.
This provides support for a conjecture of Archdeacon et al. and resolves a problem of Salazar.