2020/02/23 by Balogh, Jozsef, Bollobas, Bela, Narayanan, Bhargav · 1 citation
#05A16 #05C35 #05C65 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.09995
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.