I've got a 38T on my bike with a 203mm rear disc, and someone else here managed to get a 40 to work as well. If the dropouts can manage to move the rotor out enough and the caliper and mounting bracket have some adjustment range to them both vertical and horizontal, it is possible to fit a larger than 36 tooth. Just takes the right combination of bike and parts.
If the bike has a caliper mount between the 2 dropout tubes, the chain is not present to cause clearance issues with the caliper and allows for pretty much any size rear sprocket.