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  • Hypercellular graphs: partial cubes without ▫$Q_3^-$▫ as partial cube minor
    Chepoi, Victor ; Knauer, Kolja ; Marc, Tilen
    We investigate the structure of isometric subgraphs of hypercubes (i.e., partial cubes) which do not contain finite convex subgraphs contractible to the 3-cube minus one vertex ▫$Q_3^-$▫ (here ... contraction means contracting the edges corresponding to the same coordinate of the hypercube). Extending similar results for median and cellular graphs, we show that the convex hull of an isometric cycle of such a graph is gated and isomorphic to the Cartesian product of edges and even cycles. Furthermore, we show that our graphs are exactly the class of partial cubes in which any finite convex subgraph can be obtained from the Cartesian products of edges and even cycles via successive gated amalgams. This decomposition result enables us to establish a variety of results. In particular, it yields that our class of graphs generalizes median and cellular graphs, which motivates naming our graphs hypercellular. Furthermore, we show that hypercellular graphs are tope graphs of zonotopal complexes of oriented matroids. Finally, we characterize hypercellular graphs as being median-cell -- a property naturally generalizing the notion of median graphs.
    Vir: Discrete mathematics. - ISSN 0012-365X (Vol. 343, iss. 4, Apr. 2020, art. 111678 (28 str.))
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2020
    Jezik - angleški
    COBISS.SI-ID - 25235203

    Povezava(-e):

    https://doi.org/10.1016/j.disc.2019.111678
    DOI

vir: Discrete mathematics. - ISSN 0012-365X (Vol. 343, iss. 4, Apr. 2020, art. 111678 (28 str.))
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