In a large bowl toss together cabbage, carrot, and onion; set aside. In a small bowl whisk together vinegar, lime juice, oil, honey, garlic, ginger, and dill weed. Pour vinegar mixture over cabbage mixture; toss to coat. Let stand at room temperature for 15 minutes, stirring occasionally, or cover and refrigerate in an airtight container for up to 24 hours before serving.
Meanwhile, prepare frankfurters according to package directions. Place each cooked frankfurter in a bun. Top with cabbage mixture. Makes 8 servings.