Quick Gossiping by Multi-Telegraphs

Entringer and Slater /1/ considered the following communication problem: Suppose each of n≥2 points (persons) 1,2,...,n knows are item of information which is not known to all the others. They exchange information using telegrams arranged in consecutive rounds whereby in every round: (1) each point can either send or receive telegrams, i.e. it is impossible for a given point to send some and to receive other telegrams in the same round; (2) any pair r,s∈V={1,2,.,..,n} is allowed to communicate by a telegram, and if s sends a telegram to r, then in that round, r learns all information which s knows at this time; (3) every point can communicate with at most k different points (k≥1), i.e. depending on whether it is a sender or a receiver in that round the point can either send at most k telegrams or receive at most k telegrams.