Graphs with at most one crossing

Agradecimentos: The first author was supported by FAPESP (Brazil) Proc. 2015/04385-0, 2014/14375-9 and 2015/11937-9, CNPq (Brazil) Proc. 311373/2015-1. The second author was supported by CONACyT (Mexico) and by the ISTplus Fellowship (Austria). The third author was supported by NSERC (Canada) Grant No. 41705-2014 057082. The fourth author was supported by CNPq Proc. 311373/2015-1, CNPq Proc. 425340/2016-3 and FAPESP Proc. 2015/11937-9. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 754411 Abstract: The crossing number of a graph G is the least number of crossings over all possible drawings of G. We present a structural characterization of graphs with crossing number one CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP Fechado