(UL)
  • Packing triangles in weighted graphs
    Chapuy, Guillaume ...
    Tuza conjectured that for every graph ▫$G$▫ the maximum size ▫$\nu$▫ of a set of edge-disjoint triangles and minimum size ▫$\tau$▫ of a set of edges meeting all triangles satisfy ▫$\tau \leq 2\nu$▫. ... We consider an edge-weighted version of this conjecture, which amounts to packing and covering triangles in multigraphs. Several known results about the original problem are shown to be true in this context, and some are improved. In particular, we answer a question of Krivelevich, who proved that ▫$\tau \leq 2\nu^*$▫ (where ▫$\nu^*$▫ is the fractional version of ▫$\nu$)▫ and asked whether this is tight. We prove that ▫$\tau \leq 2\nu^*-\frac{1}{\sqrt{6}}\sqrt{\nu^*}$▫ and show that this bound is essentially best possible.
    Vir: SIAM journal on discrete mathematics. - ISSN 0895-4801 (Vol. 28, no. 1, 2014, str. 226-239)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 17210713

vir: SIAM journal on discrete mathematics. - ISSN 0895-4801 (Vol. 28, no. 1, 2014, str. 226-239)

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