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  • Natural realizations of sparsity matroids
    Streinu, Ileana ; Theran, Louis
    A hypergraph ▫$G$▫ with ▫$n$▫ vertices and ▫$m$▫ hyperedges with ▫$d$▫ endpoints each is ▫$(k,\ell )$▫-sparse if for all sub-hypergraphs ▫$G^\prime$▫ on ▫$n^\prime$▫ vertices and ▫$m^\prime$▫ edges, ... ▫$m^\prime \leq kn^\prime - \ell$▫. For integers ▫$k$▫ and ▫$\ell$▫ satisfying ▫$0 \leq \ell \leq dk - 1$▫, this is known to be a linearly representable matroidal family. Motivated by problems in rigidity theory, we give a new linear representation theorem for the ▫$(k,\ell)$▫-sparse hypergraphs that is natural; i.e., the representing matrix captures the vertex-edge incidence structure of the underlying hypergraph ▫$G$▫.
    Vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 141-151)
    Vrsta gradiva - članek, sestavni del
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 16265561

    Povezava(-e):

    http://amc.imfm.si/index.php/amc/article/view/197
    Digitalna knjižnica Slovenije - dLib.si

vir: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 4, no. 1, 2011, str. 141-151)

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