One Piece's power system is based on devil fruits and haki.
While many One Piece characters like Luffy and the Marine Admirals hone their devil fruit abilities along with haki, swordsmen like Shanks and Mihawk have always focused more on improving all forms of haki.
In One Piece, Mihawk holds the title of the world's greatest swordsman. However, the true extent of his power remains unknown.
In the One Piece manga, the character's power system, information, and relationships are often difficult to keep track of, which is why Vivre Cards are so useful, as they act as information pages in the One Piece databook.
In Mihawk's Vivre Card, there is currently no information about him using Conqueror's Haki, although most of the strongest characters possess this ability.
Fans have been divided on this issue, with some believing that any important information will not be revealed in the Vivre Cards. While others believe that Mihawk is not one of the main characters.
As one fan shared: “I guess they won't reveal Mihawk has Haoshoku Haki until later. I highly doubt he could face Shanks without it.”
In the past, Shanks and Mihawk fought many times, but it was unclear who won. Even someone like Whitebeard, when talking to Shanks in chapter 434, said that Mihawk's battle with Shanks was still fresh in his mind. This proves that their battle must have been very epic, to leave such a deep impression on Whitebeard. If Mihawk didn't have Haoshoku Haki, could he have fought Shanks to that extent?
“Zoro and Garp's Vivre Cards do not confirm Haoshoku Haki even though we know both characters have it. Mihawk's case may be similar.”another wrote.
After the Shichibukai disbanded, Mihawk's bounty was set at 3,590,000,000 Belly, higher than that of Yonko Luffy with about 3 billion Belly, further showing that Mihawk's strength is not to be trifled with.
Now, to know clearly whether Mihawk has Conqueror's Haki or not, we have to wait for confirmation from author Oda.