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- W4302048043 abstract "The independence number $alpha(H)$ of a hypergraph $H$ is the maximum cardinality of a set of vertices of $H$ that does not contain an edge of $H$. Generalizing Shearer's classical lower bound on the independence number of triangle-free graphs (J. Comb. Theory, Ser. B 53 (1991) 300-307), and considerably improving recent results of Li and Zang (SIAM J. Discrete Math. 20 (2006) 96-104) and Chishti et al. (Acta Univ. Sapientiae, Informatica 6 (2014) 132-158), we show that $$alpha(H)geq sum_{uin V(H)}f_r(d_H(u))$$ for an $r$-uniform linear triangle-free hypergraph $H$ with $rgeq 2$, where begin{eqnarray*} f_r(0)&=&1mbox{, and } f_r(d)&=&frac{1+Big((r-1)d^2-dBig)f_r(d-1)}{1+(r-1)d^2}mbox{ for $dgeq 1$.} end{eqnarray*}" @default.
- W4302048043 created "2022-10-06" @default.
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- W4302048043 date "2015-07-15" @default.
- W4302048043 modified "2023-09-25" @default.
- W4302048043 title "Independence in Uniform Linear Triangle-free Hypergraphs" @default.
- W4302048043 doi "https://doi.org/10.48550/arxiv.1507.04323" @default.
- W4302048043 hasPublicationYear "2015" @default.
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