What is wrong with giving flowers to someone on Shabbat? May one put flowers in a vase? What Melacha would this be?

Conducting transfer of property ("kinyan") is not allowed on Shabbat, with the exception of foodstuffs which could be served at the meal (though they don't have to be served). Flowers are no exception, though thaey may be given before Shabbat. Placing flowers in a vase with water is not allowed, since it appears to be "watering" which is a subcategory of planting. (It is not actually planting, but similar enough for the Rabbis to tell us not to do it.