Can HIV/AIDS be transmitted through saliva?

My daughters' grandfather, (their father's adoptive father,) has AIDS and knowing how young children, (they are 3 & 4), tend to get bumps, scrapes, and bruises all the time while they are playing, and then, imagining an adult playing with a child, you know, the way they 'play bite' the child's fingers to get them to smile? I'm forced to wonder, can AIDS be transferred through saliva if the saliva comes into contact with the blood stream? If there was a small cut on the finger or hand, and the play bite resulted in very much drool at all, saliva could easily fill the open cut. I need to know if the virus in the saliva itself is strong enough to infect someone when brought into contact directly with an open cut or scrape? This scenario has never come up because the children are obviously always supervised around the grandfather, but as their mother, I just can't help but worry. I think with this one, I have just cause.