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A very short proof of Sidorenko's inequality for counts of homomorphism between graphs
Lukas Lüchtrath, Christian Mönch · 2024-08-02 · via math.PR updates on arXiv.org

We provide a very elementary proof of a classical extremality result due to Sidorenko (Discrete Math. 131.1-3, 1994), which 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 $H$.

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