I think Zoro and Mihawk will not fight again, I can't remember also Mihawk claiming that he is the strongest swordsman on the world of one piece therefore only people knows about he's skill, scared or amazed seeing him will usually share and spread this title to everybody. Just like Zoro he's not claiming that he's a pirate hunter but the pirates usually calls him with that title and spread to everyone, and again I don't think Mihawk and Zoro will fight again, another reason is the 2 years timeskip by the time Mihawk trained Zoro they're probably close friends now like Luffy and Rayleigh. Mihawk already knows himself that he is not the Strongest Swordsman but for the new era pirates he is. Mihawk knows who is the Strongest Swordsman and that is the one of the Five Elders (Gorosei) that bald one who always held a sword that is said to be the strongest swords of all swords in one piece. Zoro is probably unaware of this. and I truly believe this would be the last enemy of Zoro to become the Strongest Swordsman. Mihawk will not interfere to the Final WAR he's always been a hybrid character throughout the series probably if he's involved then he will. To cut the long story short, after Zoro defeats the BALD MAN SUNGLASSES GOROSEI the news will reach out to Mihawk immediately, and once they meet again Mihawk will definitely acknowledge Zoro.
AND THE REST IS HISTORY
What do you guys thinkk??
AND THE REST IS HISTORY
What do you guys thinkk??