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  • Obstructions for two-vertex alternating embeddings of graphs in surfaces
    Mohar, Bojan, 1956- ; Škoda, Petr
    A class of graphs that lies strictly between the classes of graphs of genus (at most)▫ $k-1$▫ and ▫$k$▫ is studied. For a fixed orientable surface ▫$\mathbb{S}_k$▫ of genus ▫$k$▫, let ... ▫$\mathcal{A}_{xy}^k$▫ be the minor-closed class of graphs with terminals ▫$x$▫ and ▫$y$▫ that either embed into ▫$\mathbb{S}_{k-1}$▫ or admit an embedding ▫$\Pi$▫ into ▫$\mathbb{S}_k$▫ such that there is a ▫$\Pi$▫-face where ▫$x$▫ and ▫$y$▫ appear twice in the alternating order. In this paper, the obstructions for the classes ▫$\mathcal{A}_{xy}^k$▫ are studied. In particular, the complete list of obstructions for ▫$\mathcal{A}_{xy}^1$▫ is presented.
    Source: European journal of combinatorics = Journal européen de combinatoire = Europäische Zeitschrift für Kombinatorik. - ISSN 0195-6698 (Vol. 59, 2017, str. 96-113)
    Type of material - article, component part
    Publish date - 2017
    Language - english
    COBISS.SI-ID - 17761369

    Link(s):

    http://dx.doi.org/10.1016/j.ejc.2016.08.001

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