  This paper studies the problem of broadcasting in synchronous point-to-point
networks, where one initiator owns a piece of information that has to be
transmitted to all other vertices as fast as possible. The model of fractional
dynamic faults with threshold is considered: in every step either a fixed
number $T$, or a fraction $\alpha$, of sent messages can be lost depending on
which quantity is larger.
  As the main result we show that in complete graphs and hypercubes it is
possible to inform all but a constant number of vertices, exhibiting only a
logarithmic slowdown, i.e. in time $O(D\log n)$ where $D$ is the diameter of
the network and $n$ is the number of vertices.
  Moreover, for complete graphs under some additional conditions (sense of
direction, or $\alpha<0.55$) the remaining constant number of vertices can be
informed in the same time, i.e. $O(\log n)$.
