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  • A VERY SHORT PROOF OF SIDORENKO’S INEQUALITY FOR COUNTS OF HOMOMORPHISMS BETWEEN GRAPHS

  • Part of
  • LUKAS LÜCHTRATH, CHRISTIAN MÖNCH
  • Journal:
    Bulletin of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    14 April 2025, pp. 1-5
    • Article
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  • A fundamental extremality result due to Sidorenko [‘A partially ordered set of functionals corresponding to graphs’, Discrete Math. 131(1–3) (1994), 263–277] states that among all connected graphs G on k vertices, the k-vertex star maximises the number of graph homomorphisms of G into any graph H. We provide a new short proof of this result using only a simple recursive counting argument for trees and Hölder’s inequality.