We study the relation between the rate at which rumors spread throughout a graph and the vertex expansion of the graph. We consider the standard rumor spreading protocol where every node chooses a random neighbor in each round and the two nodes exchange the rumors they know. For any n-node graph with vertex expansion , we show that this protocol spreads a rumor from a single node to all other nodes in rounds with high probability. Further, we construct graphs for which rounds are needed. Our results complement a long series of works that relate rumor spreading to edge-based notions of expansion, resolving one of the most natural questions on the connection between rumor spreading and expansion.
Guest: George Giakkoupis
Host: Chen Avin