Yes, kissing involves the exchange of DNA. When you kiss your partner, you not only exchange bacteria and mucus, but also some of your genetic code. This DNA can linger in their mouth for at least an hour.
While the exchange of DNA during a kiss might be interesting, it doesn't necessarily mean that kissing directly influences mate selection. Some studies suggest that kissing may be a way to assess the genetic compatibility of a potential partner, as humans are drawn to the scents of individuals with different genetic makeup, specifically those carrying different codes for their immune system.
However, it is important to note that the amount of DNA transferred during a kiss is relatively small, and it's unlikely to have a significant impact on the overall genetic makeup of the recipient. The primary function of kissing seems to be social and emotional rather than purely genetic.