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Sheldon has a table
Sheldon's table isn't up to date with modern thinking, unsurprisingly considering how little opportunity he has had to bring it up to date these past 6 years. My edit of Sheldon's table is probably more in line with what tyre and rim manufacturers are recommending these days
At the limit, you can probably get away with anything where the tyre sidewall extends outside the inner width of the rim.
gbj_tester
@Khornight2
I doubt a 20mm tyre will seat properly on a 19mm rim... Sheldon has a table that says the smaller tyre on a 19mm rim should be 28mm!