| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4656994 | Journal of Combinatorial Theory, Series B | 2011 | 16 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
