DS18B20 uses 1-wire as its communication interface. The number of devices that can be connected to the bus depends on multiple factors. Firstly, it depends on the drive strength of the 1-wire master. In addition, a lot of other factors need to be considered, including the network topology and the material of the wire.
The application note in the following link discusses the topic in more detail:   
There is another App Note 4206 discussing how to select a proper 1-wire master, which may serve as a reference. there are too many slave devices and the drive strength of the master is limited, one solution is to design the system to switch between multiple 1-wire networks.