Unexpected behaviour of crossing sequences

作者：DeVos Matt^*; Mohar Bojan; Samal Robert

来源：Journal of Combinatorial Theory - Series B, 2011, 101(6): 448-463.

DOI：10.1016/j.jctb.2010.12.002

• Crossing number
• Torus

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.

• 出版日期2011-11