Meaning : A fiercely disputed contest.
Example :
Their rancor dated from a political dogfight between them.
A real dogfight for third place.
A prolonged dogfight over their rival bids for the contract.
Meaning : An aerial engagement between fighter planes.
Meaning : A violent fight between dogs (sometimes organized illegally for entertainment and gambling).
Meaning : Arrange for an illegal dogfight.
Meaning : Engage in an aerial battle with another fighter plane.