Weakly Norming Graphs are Edge-Transitive


Let be the class of bounded measurable symmetric functions on [0, 1]2. For a function h ∈ ℋ and a graph G with vertex set [v1,⌦,vn} and edge set E(G), define

$${t_G}(h) = \int \cdots \int {\prod\limits_{{\rm{\{ }}{v_i}{\rm{,}}{v_j}{\rm{\} }} \in E(G)} {h({x_i},{x_j})\;d{x_1} \cdots d{x_n}} } .$$

Answering a question raised by Conlon and Lee, we prove that in order for tG(∣h∣)1/∣E(G)∣ to be a norm on , the graph G must be edge-transitive.

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I would like to thank Joonkyung Lee for helpful discussions, and the three anonymous referees for their careful reading of the article and valuable suggestions.

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Correspondence to Alexander Sidorenko.

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Sidorenko, A. Weakly Norming Graphs are Edge-Transitive. Combinatorica 40, 601–604 (2020). https://doi.org/10.1007/s00493-020-4468-3

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Mathematics Subject Classification (2010)

  • 05C22
  • 05C60
  • 15A60