Counting independent sets in hypergraphs

@article{Cooper2014CountingIS,
  title={Counting independent sets in hypergraphs},
  author={Jeff Cooper and Kunal Dutta and Dhruv Mubayi},
  journal={Combinatorics, Probability & Computing},
  year={2014},
  volume={23},
  pages={539-550}
}
Let G be a triangle-free graph with n vertices and average degree t. We show that G contains at least e(1−n −1/12) 1 2 n t ln t( 1 2 ln t−1) independent sets. This improves a recent result of the first and third authors [8]. In particular, it implies that as n→∞, every triangle-free graph on n vertices has at least e(c1−o(1)) √ n lnn independent sets, where c1 = √ ln 2/4 = 0.208138... Further, we show that for all n, there exists a triangle-free graph with n vertices which has at most e(c2+o(1… CONTINUE READING
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