The number of independent sets in an irregular graph

@article{Sah2019TheNO,
  title={The number of independent sets in an irregular graph},
  author={Ashwin Sah and Mehtaab Sawhney and David Stoner and Yufei Zhao},
  journal={J. Comb. Theory, Ser. B},
  year={2019},
  volume={138},
  pages={172-195}
}
  • Ashwin Sah, Mehtaab Sawhney, +1 author Yufei Zhao
  • Published 2019
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • Abstract Settling Kahn's conjecture (2001), we prove the following upper bound on the number i ( G ) of independent sets in a graph G without isolated vertices: i ( G ) ≤ ∏ u v ∈ E ( G ) i ( K d u , d v ) 1 / ( d u d v ) , where d u is the degree of vertex u in G . Equality occurs when G is a disjoint union of complete bipartite graphs. The inequality was previously proved for regular graphs by Kahn and Zhao. We also prove an analogous tight lower bound: i ( G ) ≥ ∏ v ∈ V ( G ) i ( K d v + 1… CONTINUE READING

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