= Jones polynomial breadth bound for a disconnected diagram
{c}
{title2=$\operatorname{br}V_L\leq n+k-1$}
Here $n$ is the crossing count and $k$ is the number of connected components of the planar <link diagram>, not necessarily the number of <link> components. The all-$A$ and all-$B$ state counts satisfy $s_A+s_B\leq n+2k$, by summing the <Turaev surface> <Euler characteristic> bound over projection components. The <Kauffman bracket breadth bound> and $t=A^{-4}$ give the displayed bound. It is sharp for an <unlink> diagram with $n=0$, whose <Jones polynomial> has <breadth of a Laurent polynomial> $k-1$.
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