Look at the Princess Part I: A Kiss Is But a Kiss

Moya arrives at a planet where the people test their genetic compatibility by kissing. Crichton kisses a princess, who is next in line for the throne, and discovers that his DNA is a perfect match for her. He must now marry her and they will rule together. This is against the wishes of her brother, who is second in line for the throne -- conspiring with a Scarran.