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- W4287814523 abstract "Generalizing work on graphs, Chang and Roussel introduced $k$-power domination in hypergraphs and conjectured the upper bound for the $k$-power domination number for $r$-uniform hypergraphs on $n$ vertices was $frac{n}{r+k}$. This upper bound was shown to be true for simple graphs ($r=2$) and it was further conjectured that only a family of hypergraphs, known as the squid hypergraphs, attained this upper bound. In this paper, the conjecture is proven to hold for hypergraphs with $r=3$ or $4$; but is shown to be false, by a counterexample, for $rgeq 7$. Furthermore, we show that the squid hypergraphs are not the only hypergraphs that attain the original upper bound. Finally, a new upper bound is proven for $rgeq 3$." @default.
- W4287814523 created "2022-07-26" @default.
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- W4287814523 date "2020-04-16" @default.
- W4287814523 modified "2023-09-25" @default.
- W4287814523 title "An upper bound for the $k$-power domination number in $r$-uniform hypergraphs" @default.
- W4287814523 doi "https://doi.org/10.48550/arxiv.2004.07918" @default.
- W4287814523 hasPublicationYear "2020" @default.
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