This paper studies the problem of upper bounding the number of independent sets in a graph, expressed in terms of its degree distribution. For bipartite regular graphs, Kahn (2001) established a tight upper bound using an information-theoretic approach, and he also conjectured an upper bound for general graphs. His conjectured bound was recently proved by Sah et al. (2019), using different techniques not involving information theory. The main contribution of this work is the extension of Kahn's information-theoretic proof technique to handle irregular bipartite graphs. In particular, when the bipartite graph is regular on one side, but it may be irregular in the other, the extended entropy-based proof technique yields the same bound that was conjectured by Kahn (2001) and proved by Sah et al. (2019).

翻译：本文研究了图表中独立组数的上层界限问题,以度分布方式表示。对于两边普通图,Kahn(2001年)使用信息理论方法设定了一个紧紧的上层界限,他也对一般图数进行了猜测。他所推测的界限最近由Sah等人(2019年)用不包含信息理论的不同技术加以证明。这项工作的主要贡献是将Kahn的信息理论证据技术扩展至处理非正常的双边图。特别是,当两边图在一面是常规的,但在另一面可能是不正常的时,扩展的基于英特罗比的证据技术产生与Kahn(2001年)所预测的和Sah等人(2019年)所证明的相同的界限。