  Minimum Bisection denotes the NP-hard problem to partition the vertex set of
a graph into two sets of equal sizes while minimizing the width of the
bisection, which is defined as the number of edges between these two sets. We
first consider this problem for trees and prove that the minimum bisection
width of every tree $T$ on $n$ vertices satisfies $MinBis(T) \leq 8 n \Delta(T)
/ diam(T)$. Second, we generalize this to arbitrary graphs with a given tree
decomposition $(T,X)$ and give an upper bound on the minimum bisection width
that depends on the structure of $(T,X)$. Moreover, we show that a bisection
satisfying our general bound can be computed in time proportional to the
encoding length of the tree decomposition when the latter is provided as input.
