Final answer:
The Rome IV criteria for cyclic vomiting syndrome includes recurrent, severe vomiting episodes, which is option (c). It does not require fever, persistent diarrhea, or involve focal neurological deficits.
Step-by-step explanation:
The Rome IV criteria for cyclic vomiting syndrome (CVS) specifically involve recurrent, severe vomiting episodes that are hallmark symptoms of the condition. These episodes are stereotypical in nature and occur at least one week apart. CVS is diagnosed based on a history of three or more discrete episodes of vomiting over the previous year, without an apparent cause, and with symptom-free intervals.
Option (a) that requires a fever is not part of the Rome IV criteria for CVS as fever is not a defining characteristic. Also, CVS does not typically include persistent diarrhea (option b), nor does it involve focal neurological deficits (option d), which are more commonly associated with other neurological conditions.
Therefore, the characteristic that fits the Rome IV criteria for CVS is option (c), which features recurrent, severe vomiting episodes.