  For $S\subseteq V(G)$ with $|S|\ge 2$, let $\kappa_G (S)$ denote the maximum
number of internally disjoint trees connecting $S$ in $G$. For $2\le k\le n$,
the generalized $k$-connectivity $\kappa_k(G)$ of an $n$-vertex connected graph
$G$ is defined to be $\kappa_k(G)=\min \{\kappa_G(S): S\in V(G) \mbox{ and }
|S|=k\}$. The generalized $k$-connectivity can serve for measuring the fault
tolerance of an interconnection network. The bubble-sort graph $B_n$ for $n\ge
2$ is a Cayley graph over the symmetric group of permutations on $[n]$
generated by transpositions from the set $\{[1,2],[2,3],\dots, [n-1,n]\}$. In
this paper, we show that for the bubble-sort graphs $B_n$ with $n\ge 3$,
$\kappa_4(B_n)=n-2$.
