Better Bounds for Perpetual Gossiping

In the perpetual gossiping problem, introduced by Liestman and Richards, information may be generated at any time and at any vertex of a graph G; adjacent vertices can communicate by telephone calls. We define Wk(G) to be the minimum w such that, placing at most k calls each time unit, we can ensure that every piece of information is known to every vertex within w time units of its generation. Improving upon results of Liestman and Richards, we give bounds on Wk(G) for the cases when G is a path, cycle or hypercube.