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- W2006160791 abstract "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 $tau leq 2nu$. 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 $tau leq 2nu^*$ (where $nu^*$ is the fractional version of $nu$) and asked whether this is tight. We prove that $tau leq 2nu^*-frac{1}{sqrt{6}}sqrt{nu^*}$ and show that this bound is essentially best possible." @default.
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- W2006160791 date "2014-01-01" @default.
- W2006160791 modified "2023-10-14" @default.
- W2006160791 title "Packing Triangles in Weighted Graphs" @default.
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- W2006160791 doi "https://doi.org/10.1137/100803869" @default.
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