Uh no Its Mihawk who gave up.
http://www.onemanga.com/One_Piece/96/16/
Shanks was ready to go anytime
That scene shows me that most likely Mihawk always came to shanks to duel not the other way around
I just thought of something
Imagine what zoro would do if Mihawk lost his good arm! He...
Since everyone is using the strongest swordsman argument
Would you say Mihawk is stronger then Rayleigh since he also seems to be a swordsmen who also uses haki