The Lexington-style North Carolina side dish that uses ketchup instead of mayonnaise is red slaw.
Red slaw, also called barbecue slaw, is a cabbage-based condiment strongly associated with Lexington-style North Carolina barbecue. Its dressing uses vinegar, ketchup, water, and seasonings rather than mayonnaise, giving the slaw its reddish color and a tangy, lightly sweet flavor. It is commonly served with pulled pork, barbecue sandwiches, hot dogs, and hamburgers.
The lack of mayonnaise is more than a flavor preference. Vinegar-based red slaw is easier to serve outdoors and can keep longer without refrigeration than traditional mayonnaise-based coleslaw. Recipes differ by cook and region; onion, sugar, mustard seed, black pepper, and other spices may be added.
In parts of the Southeast, mayonnaise-based coleslaw is informally called white slaw to distinguish it from red slaw. That contrast can cause confusion, because “slaw” alone may refer to several preparations. Chow-chow is another Southern cabbage relish, but it is generally pickled and served as a condiment rather than being the characteristic Lexington barbecue slaw.