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An Information-Theoretic Proof of a Bound on the Number of Independent Sets in Bipartite Graphs

12/22/2020

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by Igal Sason, et al.

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The present paper provides an information-theoretic proof of Kahn's conjecture (2001) for a tight upper bound on the number of independent sets in a graph, where our proof applies to bipartite graphs that are regular on one side (the other side may be irregular). It extends the entropy-based proof for regular bipartite graphs (Kahn, 2001). This conjecture has been recently proved for general graphs by a group at MIT (2019), utilizing an interesting approach which is unrelated to information theory.

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