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6
votes
Accepted
On a limit involving a transform of the chromatic polynomial
Here is a heuristic argument which perhaps someone can make
rigorous. I write $v_n=v(G_n)$ and $e_n=e(G_n)$. Let
$$ \chi_{G_n}(x) =
x^{v_n}-c_{n,v_n-1} x^{v_n-1}+c_{n,v_n-2}x^{v_n-2}-\cdots. $$
I c …