Unexpected behaviour of crossing sequences

The nth 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.

• Type: Journal
• Year: 2008
• Where: ENDM
• Authors: Matt DeVos, Bojan Mohar, Robert Sámal
• Keywords: ENDM 2008, Minimum Number, Nth Crossing Number, Orientable Surface