Remove heavy outer dark green leaves from cabbage; cut in half lengthwise through core.
With a long sharp knife, slice the green part into long shreds that are as thin as possible; cut enough cabbage to make 6 cups firmly packed.
Use the green part only for the coleslaw; the thick white part can be used for cooking other dishes.
With a fork. gradually stir vinegar into mayonnaise keeping it smooth.
Add sugar and salt; mix well. Pour over cabbage and mix thoroughly.
Refrigerate for 3 hours or until chilled and flavors have blended. Good for 8 persons.