The World of Ribs : The Great Rib Side Dish--Coleslaw : Cooking: Its history is muddled and its variations are many. But there’s probably a version for every taste and temperament.

Coleslaw is one of those all-American dishes that was, of course, invented somewhere else--in this case, Britain or Holland or Germany, depending on whom you ask, gets the credit. Some books insist the dish was served first in ancient Rome.

There’s even disagreement on whether coleslaw is a salad, a relish, an hors d’oeuvre or a side dish. And nobody is quite sure how the term “coleslaw” turned up in America. In Dutch, cabbage salad is koolsla . In German kohl (as well as kraut ) means “cabbage” and slau means “salad.” “Cole” is old English for kohl . But many early American cookbooks referred not to cole slaw but cold slaw.

The only constant in true coleslaw is the cabbage. Red, green or white will do. And the cabbage is almost always shredded, though the fanciest coleslaw served in Los Angeles--Michel Richard’s crab coleslaw at Citrus--uses cabbage as a beautiful wrapper. For the dressing, some swear by mayonnaise, others by vinegar, sour cream, even whipping cream.

Coleslaw may come cold, it may come hot. We’ve even seen a recipe for frozen coleslaw. Some slaws should be eaten immediately, others let to set in the refrigerator for a day. Dry mustard, black pepper and sugar are often tossed into the mix, but so are onions, carrots, sweet green peppers, roasted peppers, pickle relish, garlic, daikon, even jalapenos . Celery and caraway seeds are good friends of coleslaw.

In his book, “American Cookery,” James Beard approved of the use of carrots, green pepper and seafood in his coleslaw, but there was a limit to his tolerance for experimentation:

“Pineapple and white grapes hold no brief for this palate, and I need hardly comment on one writer who advised using pineapple, white grapes and tiny marshmallows.”

Coleslaw may not be a U.S. invention, but American ingenuity has clearly left its mark.

What follows is just a small sampling of the slaws you make with a head of cabbage.