Network communication in edge-colored graphs: gossiping

A mechanism for scheduling communications in a network in which individuals exchange information periodically according to a fixed schedule is presented. A proper k edge-coloring of the network is considered to be a schedule of allowed communications such that an edge of color i can be used only at times i modulo k. Within this communication scheduling mechanism, the information exchange problem known as gossiping is considered. It is proved that there is a proper k edge-coloring such that gossip can be completed in a path of n edges in a certain time for n⩾k⩾1. Gossip can not be completed in such a path any earlier under any proper k edge-coloring. In any tree of bounded degree Δ and diameter d, gossip can be completed under a proper Δ edge-coloring in time (Δ-1)d +1. In a k edge-colored cycle of n vertices, other time requirements of gossip are determined