Is it OK to give melon or watermelon to my dog?

My dog seems to have a pion for melon and watermelon. Everytime she sees us eat some she will start dribbling in anticipation. We only eat it like once a week and I would only give her a really small triangle of very fresh stuff and make sure there are no seeds in it. Do you think it's OK? Can't be worse that some of treats sold in the shops can they? She never has had any adverse reaction so far