Counting independent sets in regular hypergraphs

Jozsef Balogh; Bela Bollobas; Bhargav Narayanan

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arXiv · 2002.09995

Counting independent sets in regular hypergraphs

Jozsef Balogh·Bela Bollobas·Bhargav Narayanan

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Abstract

Amongst $d$-regular $r$-uniform hypergraphs on $n$ vertices, which ones have the largest number of independent sets? While the analogous problem for graphs (originally raised by Granville) is now well-understood, it is not even clear what the correct general conjecture ought to be; our goal here is propose such a generalisation. Lending credence to our conjecture, we verify it within the class of `quasi-bipartite' hypergraphs (a generalisation of bipartite graphs that seems natural in this context) by adopting the entropic approach of Kahn.

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BibTeX RIS

Jozsef Balogh, Bela Bollobas, Bhargav Narayanan. 2020-02-23. Counting independent sets in regular hypergraphs. https://arxiv.org/abs/2002.09995

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