Given some probability $p\in[0,1]$ is it possible to construct a graph $(G,V)$ with critical bond percolation probability $p_c = p$?

I know for example that I can get $\frac{1}{m}$ for any natural number $m$ by taking bond-percolation on the $m$-ary tree, and I know many more examples, but I can't figure out how one would construct it for arbitrary $p$.

Some ideas I have had are to try to take a Galton-Watson tree and convert that into a percolation problem on some graph... but I was only able to make this work for the $m$-ary tree above.


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