Whites should always be washed by themselves to keep colors from running. For example, clothes that are light gray should be washed with other light colors, and clothes that are dark gray should be washed in the dark pile.
Dark and light clothes need to be washed in cold water separately. By washing things in cold water, you can cut down on how much colors run into each other. Why not just mix the whites and lights together? Warm or hot water is better at getting rid of dirt than cold water, so your whites stay white, even though it doesn’t stop color bleeding as well.