What is the minimum Mac OS Partition size when using Boot Camp on a Macbook Air? And does it vary with 128GB or 256GB size hard drives?
I don't see how this would depend on the type of Mac or hard drive. Instead, it should only depend on the version of OS X that you're running.

While Apple's documentations for OS X 10.7 Lion state 7 GB as a required minimum, BootCamp 4.0.3 allows a minimum of 8GB for the OS X partition. Probably, because this includes the 650 MB for the recovery partition (end of page).