Sentence III has a modifier problem. It sounds like Alfred Nobel was the Nobel Peace Prize recipient, instead of the founder. Corrected: “...an honour that was established by Alfred Nobel.”
Sentence IV is incorrect due to subject-verb agreement: “Neither” is singular, so the verb should be “works,” but it is followed by “they would,” which is plural. This pronoun mismatch makes it incorrect.
\[
\boxed{\text{III and IV}}
\]
\bigskip