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.



Number of homomorphisms from graph $H$ to $G$ , bounds that have to do with fractional coloring number?
You are referring to [E. Friedgut and J. Kahn, On the number of copies of one hypergraph in another](https://link.springer.com/article/10.1007/BF02780332), 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](https://link.springer.com/article/10.1007/BF02761855), Israel J. Math. 38(1981), 116-130


