The Max-2SAT problem asks if at least k clauses of a 2CNF formula can be satisfied.
The Max-2SAT(at-most-3) problem is the restriction in which every variable occurs in at most 3 clauses (counting positive and negative occurrences together). It is known that this problem is APX-hard, the reference being this book. However, I can't access the book, so I can't look at the details.
The Max-2SAT(exactly-3) problem is the restriction in which every variable occurs in exactly 3 clauses, i.e. no variable occurs only twice. From this paper, I believe the problem is NP-hard. But I don't know if it's also APX-hard. Is it? Does it follows from the "at-most-3" case? If not, I'd like to know how many of the n variables occur only twice, and not three times.