  We study the broadcast problem on dynamic networks with $n$ processes. The
processes communicate in synchronous rounds along an arbitrary rooted tree. The
sequence of trees is given by an adversary whose goal is to maximize the number
of rounds until at least one process reaches all other processes. Previous
research has shown a $\lceil{\frac{3n-1}{2}}\rceil-2$ lower bound and an
$O(n\log\log n)$ upper bound. We show the first linear upper bound for this
problem, namely $\lceil{(1 + \sqrt 2) n-1}\rceil \approx 2.4n$. Our result
follows from a detailed analysis of the evolution of the adjacency matrix of
the network over time.
