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Counting independent sets in regular hypergraphs
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-01-13 , DOI: 10.1016/j.jcta.2021.105405 József Balogh , Béla Bollobás , Bhargav Narayanan
中文翻译:
计数规则超图中的独立集
更新日期:2021-01-13
Journal of Combinatorial Theory Series A ( IF 0.9 ) Pub Date : 2021-01-13 , DOI: 10.1016/j.jcta.2021.105405 József Balogh , Béla Bollobás , Bhargav Narayanan
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 to 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.
中文翻译:
计数规则超图中的独立集
在n个顶点上的d-正则r-一致超图中,哪个具有最大的独立集?尽管现在已经很好地理解了图的类似问题(最初由Granville提出),但是甚至不清楚确切的一般猜想应该是什么。我们这里的目标是提出这样一个概括。通过使用Kahn的熵方法,在我们的“准二分”超图类(在这种情况下看起来很自然的二分图的一般化)的类中证明了我们的猜想。