Walter New gossips and telephones. Congressus Numerantium, No. The connections between the elements in the initial problem form a complete and undirected graph. In general, the graph which represents the connections is directed and not complete or undirected and not complete. A conjecture of Golumbic dealing with undirected graphs without 4-cycles is considered and the author proves it for a subclass of such graphs.
Communication is done by performing telephone calls along the edges of the graph.
Every node can participate in at most one call at a time and during a call participating nodes exchange all previously accumulated information. The author proves a structural theorem concerning schemes of calls that achieve gossiping. The theorem says that calls of every such scheme can be rearranged into a sequence such that at most two calls cause each node to become fully informed and that the reverse sequence has the same property. This rather technical result has many important consequences. The author obtains well-known and important results from the theory of gossiping as easy corollaries of his theorem.