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  • Unexpected behaviour of crossing sequences
    DeVos, Matt ; Mohar, Bojan, 1956- ; Šámal, Robert
    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.
    Source: Journal of combinatorial theory. Series B. - ISSN 0095-8956 (Vol. 101, iss. 6, 2011, str. 448-463)
    Type of material - article, component part
    Publish date - 2011
    Language - english
    COBISS.SI-ID - 16051801

    Link(s):

    http://dx.doi.org/10.1016/j.jctb.2010.12.002

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