If nothing matches while applying full outer join the resultant would be (m+n).
Firstly, there is a misconception that min. would occur when nothing would match.
Min. would occur when values in tuples actually matches! And, then it would be max.(m,n).
E.g.
Consider relation A with 3 tuples and B with 5 tpl.
So, misconception says min of outer join would be if there's no match. i.e m+n = 5+3 = 8 tuples. but this is not the case to get minimum.
To get min. in full outer join:
Consider, 3 out of 3 in A matches with B's tuples
this time, resultant relation would have: 3(matched) + 2(unmatched) tuple = 5 tuples. (which is less than 8)
This is the min. case, when EVERY tuple in one of the relational table matches with tuples in other. Hence, max of (m,n).
I hope this explanation helps.