However, in the case of this specific rivalry, it's very one-sided at the current moment, since Mihawk still considers Zoro to be far beneath him in terms of power. His true rival is Shanks, who ...

Dracule Mihawk, a former Warlord and someone with the title of the World’s Strongest Swordsman, is one such character. He was introduced in Chapter 46 of the East Blue Saga.