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I once read a short paper on the following subject. Fix a graph $H$ with fractional coloring number $c$ and let $G$ be a graph with $n$ vertices and $e$ edges, with $e$,$n$ large. In terms of $n$, $e$, and $c$, we want to bound from above and below the number of homomorphisms from $H$ to $G$.

I cannot seem to find the paper. Can someone help me?

I don't remember the authors, but they thanked Gil Kalai for suggesting the connection with fractional coloring number; this is a detail that I remember, for some reason.

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You are referring to E. Friedgut and J. Kahn, On the number of copies of one hypergraph in another, Israel Journal of Mathematics 105 (1998), 251–256. For graphs this result is the very first paper of Noga Alon, On the number of subgraphs of prescribed type pf graphs with a given number of edges, Israel J. Math. 38(1981), 116-130

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  • $\begingroup$ Thanks, now I get to thank Gil Kalai as well :) $\endgroup$
    – Andy
    Commented Sep 27, 2018 at 19:49
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I found it in accident:

It is one of the results that appear here: https://www3.nd.edu/~dgalvin1/pdf/Kalamazoo_entropy.pdf

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  • $\begingroup$ Good. Please accept your own answer so that the system considers your question as solved. $\endgroup$
    – YCor
    Commented Feb 25, 2018 at 17:39
  • $\begingroup$ @YCor Okay, it is telling me I can only do so tomorrow, so I will try again then. Sorry about the spam question, I was looking hard for it. $\endgroup$
    – Andy
    Commented Feb 25, 2018 at 17:40

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