After his fight with Mihawk, Zoro was ashamed of his defeat.

Source: https://www.cbr.com/one-piece-moments-when-all-the-straw-hats-say-luffy-will-become-the-pirate-king/

From the moment Zoro stubbornly took the final swing from Yoru, fans knew Zoro would one day fight toe-to-toe with Mihawk and wrestle the title from the Warlord’s hands.

Source: https://www.cbr.com/one-piece-zoro-final-opponent-mihawk-shiryu-strongest-swordsman/

His crew draws their weapons in the face of the Warlord, but Shanks speaks to Mihawk with casual confidence as they allude to a former rivalry.

Source: https://collider.com/one-piece-season-1-unanswered-questions/

Mihawk stated during the Summit War that Luffy's ability to attract and make allies in almost no time was the most dangerous power someone on the sea could have.

Source: https://www.cbr.com/one-piece-spoilers-how-buggy-the-clown-became-yonko/

What's more interesting is how he managed to bring Mihawk and Crocodile under his leadership.

Source: https://gamerant.com/one-piece-episode-1086-release-date-what-to-expect/