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Packing triangles in weighted graphsChapuy, 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.Source: SIAM journal on discrete mathematics. - ISSN 0895-4801 (Vol. 28, no. 1, 2014, str. 226-239)Type of material - article, component part ; adult, seriousPublish date - 2014Language - englishCOBISS.SI-ID - 17210713
Author
Chapuy, Guillaume |
DeVos, Matt |
McDonald, Jessica |
Mohar, Bojan, 1956- |
Scheide, Diego
Topics
matematika |
teorija grafov |
pakiranje |
pokrivanje |
trikotniki |
mathematics |
graph theory |
packing |
covering |
triangles
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Chapuy, Guillaume | ![]() |
DeVos, Matt | ![]() |
McDonald, Jessica | ![]() |
Mohar, Bojan, 1956- | 01931 |
Scheide, Diego | ![]() |
Source: Personal bibliographies
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