I am interested in Distributed Algorithms especially in communication in network with failures.

I look for the proof of the following randomized algorithm of communication in network with failures. For me it seems like very general result in the communication, nevertheless I haven’t found the proof yet. 

**Algorithm**: Initially only vertex $v\_0$ has the message, at the end of the algorithm every vertex of the network should have the message. 

On every round every vertex that has the message choice the neighbour randomly and sends it the message.

**Assumptions**: only $f$ failures might happen on the edges between the vertices.
$T = O(\log n)$ - time complexity and the entire network will know the message with high probability, when $f<n/3$, where n - number of vertices.

I will appreciate for link or reference to the paper.