What's the minimum vent diameter required for my drain line?
I've found this: 


  Vent piping should never be less than half the diameter of the fixture
  drain it serves, and usually should be closer in size. For example,
  waste pipes of 3" and 4" diameters should be serviced by a minimum 2"
  vent pipe. And regardless of piping size, no vent should be smaller
  than 1 1/4" pipe. Dual vents which are to service more than one
  fixture should be slightly larger than required for a single fixture.


source: plumbing-basics.com