Unexpected behaviour of crossing sequences

Details Unexpected behaviour of crossing sequences Unexpected behaviour of crossing sequences

2009-11-02

arxiv.org/abs/0911.0452v2

Mathematics

Combinatorics

21 pages

Scientific paper

The n-th 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.

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