Mihawk never have a fight against:
Kaido- case never put mark on him.
Whitebeard- case in MF he said that he want to find out the difference in theirs powers, which lead to conclusion that he never challenged Whitebeard before that;
Shanks- case he fight only against two handed Shanks who became Younko and called as one of the strongest pirates only 6 years ago.
Which mean, that Mihawk never have fight against Stongest, while he fight only with scrubs like Don D Krigg