When Shanks entered the Battle of Marineford, it was to end it. All he used was a single sword to stop Akainu (considered as the strongest in the marines now) from killing Coby.
Mihawk left the battlefield saying that he had only agreed to fight Whitebeard. So is this just a normal reason for him to leave or was he scared that he would have lost to Shanks? Because, in the war Mihawk fought with other pirates except for Whitebeard so it seems a bit contradictory to what he said while leaving.
Then there was a scene where he actually tracks down Shanks just to inform him about Luffy's first bounty. Is there any particular reason behind this?
Also, does Mihawk has some relation with Shanks or is he scared of him?