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{\bf Andrew R. A. McGrae and Michele Zito}
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{\bf The Block Connectivity of Random Trees}
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Let $r$, $m$, and $n$ be positive integers such that $rm=n$.  For each
$i \in \{1, \ldots, m\}$ let $B_i = \{r(i-1)+1, \ldots, ri\}$.  The
$r$-block connectivity of a tree on $n$ labelled vertices is the
vertex connectivity of the graph obtained by collapsing the vertices
in $B_i$, for each $i,$ to a single (pseudo-)vertex $v_i$. In this
paper we prove that, for fixed values of $r$, with $r \geq 2$, the
$r$-block connectivity of a random tree on $n$ vertices, for large
values of $n$, is likely to be either $r-1$ or $r$, and furthermore
that $r-1$ is the right answer for a constant fraction of all trees on
$n$ vertices.

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