Unexpected behaviour of crossing sequences

Authors:
Matt Devos;Bojan Mohar;Robert ŠáMal
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada;Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada;Department of Mathematics, Simon Fraser University, Burnaby, B.C. V5A 1S6, Canada
Venue:
Journal of Combinatorial Theory Series B
Year:
2011

Citing 2
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GD'07 Proceedings of the 15th international conference on Graph drawing

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Abstract

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 ab0, 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.