Minimum? 1.

That is, however, not the problem. The problem is that in the event of sudden loss of significant fraction of compute power block times skyrocket, because significantly reduced compute power still has to solve problem of previous difficulty. As a consequence block times become so high that transactions are effectively blocked and the only solution to keep the network functional is a fork. Unless you imagine a scenario where everyone goes offline except for a small group and everyone slowly reconnects to the small group, most likely there would be highly partitioned network with its own bitcoin fork with enough of transaction history that a reconnect would mean collapse of local-economy.